राष्ट्रीय विज्ञान शिक्षा एवंअनुसंधान संस्थान

National Institute of Science Education and Research

National Institute of Science Education and Research

Date/Time

Venue

SMS Conference Room

Speaker

Atibur Rahaman

Affiliation

NISER Bhubaneswar

Title

Contraction procedure and braided quantum groups

Date/Time

Venue

M1

Speaker

Mr. Diptesh Kumar Saha

Title

Tomita Takesaki Theory

Date/Time

Venue

SMS conference Hall

Speaker

Diptesh Kumar Saha

Affiliation

Ph.D student

Title

FACTORILITY OF YANG-BAXTER TYPE VON NEUMANN ALGEBRA

Abstract. Bozejko and Speicher in 1994 defined a von-Neumann algebra corresponding to the qij -deformed commutation relation. In this talk we will define the von-Neumann algebra and study its factoriality under some restriction.

Date/Time

Venue

SMS seminar hall

Speaker

Archana S

Affiliation

NISER

Title

Heke Bochner Formula for Euclidean Fourier transform

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Manoj Kumar

Affiliation

IIT Delhi

Title

Harmonic analysis associated to vector measures on a compact group

It is well known that the Orlicz space is a natural generalization of the Lebesgue spaces. A vector measure is a countably additive Banach space valued measure. We discuss the Banach algebra structure on the Orlicz spaces associated to a vector measure over compact groups. We also discuss the Fourier transform of functions that are integrable with respect to vector measures over compact groups. We also introduce and study the convolution of functions from Lp-spaces associated to a vector measure.

Date/Time

Venue

Online

Speaker

Mr. Aanjaneya Rath

Affiliation

SMS, NISER

Title

Vector Bundles and Locally Free Sheaves

**Abstract: **The aim of the talk is to establish equivalence between vector bundles and locally free sheaves in algebraic geometry . We will first define geometric vector bundle and locally free sheaf separately, then we will show that both of these terms are essentially the same.

Date/Time

Venue

LH-101

Speaker

G. Priyanga

Affiliation

NISER, Bhubaneswar

Title

Mathematical Modeling

**Abstract:** In this talk, we aim to introduce the process of mathematical modeling using differential equations. Basic compartmental models for spread of infectious diseases (mathematical epidemiology) will be described. In particular, models on *the impact of awareness on epidemic outbreak* will be studied. Also, methods to analyze the local stability of the equilibrium states of the system will be discussed.

**Prerequisite:** High school level knowledge of Ordinary Differential Equations

Date/Time

Venue

PL-8

Speaker

Dr. Manas Ranjan Sahoo

Affiliation

IIT BHU

Title

Vanishing viscosity and weak asymptotic approach to systems of conservation laws admitting $\delta_\infty$-waves

Systems of Conservation laws which are not strictly hyperbolic appear in many physical applications. Generally for these systems the solution spaceis larger than the usual BVl oc space and classical Glimm-Lax Theory does not apply. We start with the non-strictly hyperbolic system(uj) t +j Xi=1( uiuj −i +12) x = 0, j = 1, 2...n.For n = 1, the above system is the celebrated Bugers equation which is well studiedby E. Hopf. For n = 2, the above system describes one dimensional model for largescale structure formation of universe. We study (n = 4) case of the above system,using vanishing viscosity approach for Riemann type initial and boundary data andpossible integral formulation, when the solution has nice structure. For certain classof general initial data we construct weak asymptotic solution developed by Panovand Shelkovich. As an application we study zero pressure gas dynamics system, namely,ut + (u. ∇)u = 0, ρt + ∇.(ρu) = 0,where ρ and u are density and velocity components respectively

Date/Time

Venue

M4

Speaker

Gururaja H. A.

Affiliation

TIFR Bangalore

Title

ON WILKING'S CRITERION FOR THE RICCI FLOW AND A RIGIDITY QUESTION IN RIEMANNIAN GEOMETRY

This talk consists of two parts; the first one dealing with a study of certain positive curvatures under the Ricci flow and the second one dealing with a rigidity question in geodesic flows.In 2010 Buchard Wilking proved that for every Ad_SO(n;C)-invariant subset S of the Lie algebraso(n;C) one can attach a notion positive curvature, which we call positive S-curvature, which is preserved by the Ricci flow. We study the properties of positive S-curvatures in reference to the Ricci flow. This part of work is in collaboration with Harish Seshadri and Soma Maity. We shall also discuss a problem motivated by blow-up considerations coming from a conjecture of Richard Schoen.In the second part of the talk we will study a rigidity question in Riemannian geometry, viz, when isRiemannian manifold determined by its geodesic flow? After a brief overview of this problem, We will present our work on the rigidity of the at cylinder. This is a joint work with C. S. Aravinda.

Date/Time

Venue

SMS Seminar Hall

Speaker

Sunil Kumar Prajapati

Affiliation

Hebrew University of Jerusalem, Israel

Title

Total Character and Irreducible Characters of p-groups

The realization of the Total Character (or Gel’fand Character) τG of a finite group G, i.e. the sum of all ordinary irreducible characters of G is an old problem in character theory of finite groups. One possible approach is to try to realize τG as a polynomial in some irreducible character of G. In this vein, K. W. Johnson has asked whether it is possible to express the total character of G as a polynomial, with integer coefficients, in a single irreducible character of G. We study for several classes of finite nilpotent groups, the problem of existence of a polynomial f(x) ∈ Q[x] such that f(χ) = τG for some irreducible character χ of G. As a consequence, we completely determine the p-groups of order at most p5 (with p odd) which admit such a polynomial. Indeed, we prove that: If G is a non-abelian p-group of order p5, then G has such a polynomial if and only if Z(G) is cyclic and (G,Z(G)) is generalized Camina pair and, we conjecture that this holds good for p-groups of any order. In the talk, we also discuss about the nonlinear irreducible characters of p-groups of order at most p5.

Date/Time

Venue

M4

Speaker

Nabin Kumar Jana

Affiliation

NISER, Bhubaneswar

Title

Radon-Nikodym theorem and conditioning

**Abstact:** Radon-Nikodym theorem of measure theory was proved in 1930 and A. N. Kolmogorov laid the foundation of modern probability in 1933 where the formal played a crucial role. In this Short Lecture Series in Mathematics (SLSM), we discuss the conditioning of probability theory in the light of Radon-Nikodym theorem. Upon the interest of the audience, we may introduce the notion of martingals and their convergence theorems. We have scheduled these lectures in the F-slot of Thursday and planned to go in accordance with the pace of the audience. Basic understanding of measure theory and functional analysis will be the prerequisite.

Date/Time

Venue

SMS Seminar Room

Speaker

Antar Bandyopadhyay

Affiliation

Indian Statistical Institute, New Delhi

Title

Random Graphs

**This is a Short Lecture Series in Mathematics (SLSM) consisting of 4 lectures of 90 minutes each. This lecture schedule in this series is the following:**

1st Lecture: Monday, October 09, 2017 - 11:30 to 13:00

2nd Lecture: Tuesday, October 10, 2017 - 11:30 to 13:00

3rd Lecture: Wednesday, October 11, 2017 - 16:30 to 18:00

4th Lecture: Thursday, October 12, 2017 - 15:30 to 17:00

**Abstract:** The first half of the mini course will be an introducing to the two classical models of random graphs (a.k.a. Erdős-Rényi random graphs) and discuss the phenomenon of phase transition. We will also discuss thresholds for monotonic properties with examples including connectivity threshold and sub-graph containment threshold.

In the second half of the course we will consider other kind of random graphs. In particular, we will discuss various models for complex networks, including Albert-Barabási preferential attachment models. We will discuss "scale-freeness", asymptotic degree distribution and "small-world phenomenon". Properties of super and sub-linear preferential attachment models and some recent developments in de-preferential attachment models will also be discussed.

If time permits we will also introduce the random geometric graphs and discuss asymptotic of the connectivity threshold.

**References:**

1. Random Graphs by Svante Janson, Tomasz Łuczak and Andrzej Rucinski;

2. Random Graphs by Béla Bollobás;

3. Random Graphs and Complex Networks by Remco van den Hofstad;

4. Random Geometric Graphs by Mathew Penrose.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Bhargab Chattopadhyay

Affiliation

Indian institute of Information Technology Vadodara

Title

Sequential Estimation of Gini Index

Economic inequality arises due to the inequality in the distribution of income and assets among individuals or groups within a society, or region or even between countries. For continuous evaluation of different economic policies taken by the government, computation of Gini index periodically for the whole country or state or region is very important. But not all countries can afford or do not collect data from households in a relatively large scale periodically.In order to compute a confidence interval of Gini index for a particular country or a region at given time, there exist fixed-sample size methods. However, for achieving a level of accuracy of estimation within some pre-specified error bound i.e. for constructing a fixed-width confidence intervals for Gini Index, no fixed sample size methodology can be used. This problem falls in the domain of sequential methodology. To date there does not exist any multi-stage or sequential procedure for constructing fixed-width confidence intervals for Gini Index.In this presentation, a fixed-width confidence interval estimation procedure of Gini index will be presented under simple random sampling scenario along with several asymptotic properties like convergence results on final sample size and also the coverage probability which are proved without any specific distributional assumption.A discussion will be made on use of other sampling schemes as well.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Venkata Krishna Kishore Gangavarapu

Affiliation

IISER Pune

Title

Representation varieties of Fuchsian groups

We estimate the dimension of the representation variety of Fuchsian groups in indefinite special orthogonal group that is of nonsplit type. In the case where the Fuchsian group is a surface group, we give an exact formula (rather that just estimate) for the dimension of the representation variety whose representation `space' is any real algebraic group.

Date/Time

Venue

M-4 (SMS)

Speaker

Dr. Shalini Bhattacharya

Affiliation

Max Planck Institute for Mathematics, Bonn

Title

On the reduction of Galois representations and local constancy with respect to weight

Abstract: Let $p$ be a prime number. The two-dimensional crystalline representations of the local Galois group $\mathrm{Gal}(\bar\Q_p|\Q_p)$ are parametrized by the pairs $(k,a)$ up to twists, where $k\geq 2$ is an integer and $a\in m_{\bar\Z_p}$, the maximal ideal in the ring of integers of $\bar\Q_p$. We are interested in studying the map$(k,a)\mapsto \bar V_{k,a}$, where $\bar V_{k,a}$ denotes the semisimplified mod $p$ reduction of a typical crystalline representation $V_{k,a}$. These reductions have been computed when $k\leq 2p+1$ or when $a$ has a small $p$-adic valuation. Using the theory of Wach modules, Laurent Berger has also shown that the map displayed above is locally constant with respect to both the variables and found an explicit bound on the radius of local constancy when %$k$ is fixed and$a$ varies (2012). However, if $a$ is fixed and $k$ varies, nothing more than the existence is known about the radius of local constancy. So we ask the following simple question: for any given $p$-adic integer $a$, how close do $k$ and $k'$ need to be in the weight space to ensure that $\bar V_{k,a}\cong\bar V_{k',a}$? We give a partial answer to this question using some explicit computations in the automorphic side of the $p$-adic and mod $p$ Local Langlands Correspondences for $\GL_2(\Q_p)$.

Date/Time

Venue

M1

Speaker

Dr. Kamalakshya Mahatab

Affiliation

NTNU, Norway

Title

Large Values of Hardy's Z-Function

Let $Z(t):=\zeta\left(\half+it\right)\chi^{-\half}\left(\half+it\right)$ be Hardy's function,where the Riemann zeta function $\zeta(s)$ has the functional equation $\zeta(s)=\chi(s)\zeta(1-s)$.Hardy's function has been used to compute the zeros of $\zeta\left(\half+it\right)$ and plays a crucial role in the theory of the Riemann zeta function.In this talk we will compute the large values of $Z(t)$ and $-Z(t)$ using the resonance method.

Date/Time

Venue

SMS seminar room

Speaker

Dr. Ramesh Prasad Panda

Affiliation

NISER, PDF

Title

Some invariants of power graphs and combinatorial properties of finite groups

Date/Time

Venue

Seminar room

Speaker

Anup Kumar Singh

Affiliation

IISER Berhampur

Title

Representation formulas for certain quadratic forms and a problem of constructing lifting maps between spaces of modular forms.

In this talk, we shall discuss the theta series associated with positive definite integral quadratic forms and some of its applications in getting formulas for the number of representations of positive integers by quadratic forms, using the theory of modular forms. The second part of this talk is about the construction of the Shimura and Shintani mappings between certain subspaces of modular forms of half-integral weights and integral weight respectively.

Date/Time

Venue

Online (Google Meet)

Speaker

Meenakshi Kansal

Affiliation

IIT Madras.

Title

Various Types of Signatures in Quantum Era

Digital signature is a fundamental cryptographic primitive. It enables an entity to validate the authenticity and integrity of a digital document. In this talk, I will be discussing Group signature, Nominative Signature and Multi-signature. Group signature scheme enables any group member to produce a signature anonymously on behalf of the group and in case of misbehavior, the signer can be traced out. In a nominative signature scheme, a nominator and a nominee jointly produce a signature such that only the nominee can verify the signature. Multisignature is a powerful cryptographic primitive that helps to reduce the bandwidth taken by N signatures from O(N ) to O(1). It provides a group of signers the ability to sign collaboratively a common message in such a way that the size of the multisignature remains the same as that of a single signature and the verifier gets convinced that the message has been signed by all the signers.

Date/Time

Venue

Online (GoogleMeet)

Speaker

K Prahlad Narasimhan

Affiliation

NISER Bhubaneswar

Title

Optimality of local search algorithms

In this talk, we discuss our attempts to solve an important open problem regarding Terrain Guarding: is the state-of-the-art polynomial-time approximation scheme for the problem [Gibson2014], a simple local search construct, optimal? In this regard, we first sketch a proof of a recent advancement in this domain by Mustafa and Jartoux [Jartoux2018]. This work proves, for geometric hitting set problems which give rise to arbitrarily large grid-like exchange graphs, that the local search algorithm is indeed optimal. In light of this result, we question if the Terrain Guarding problem can give rise to such grids. We will conclude the talk by laying out a possible plan for future work on this problem.

Date/Time

Venue

LH301

Speaker

Dr. Tanusree Khandai

Title

Integrable representations of Multiloop Lie algebras of type $A_1$

Date/Time

Venue

LH 101

Speaker

Dr. Ritwik Mukherjee

Affiliation

Dept of Mathematics, TIFR Mumbai

Title

Counting curves via Topology

Abstract: Enumerative geometry is a branch of mathematics concerned with the following question: "How many geometric objects are there that satisfy certain constraints?" The simplest example of such a question is: "How many lines pass through two distinct points?'' A more interesting example is: "How many lines are there in three dimensional space that intersect four generic lines?'' In this talk we will describe a topological method to approach enumerative questions. We will use this method to count how many degree d curves are there in CP^2 that pass through certain number of generic points and have certain singularities.

Date/Time

Venue

M5

Speaker

Panchugopal Bikram

Affiliation

ISI Kolkata

Title

Maximal abelian subalgebras in q-deformed Araki-Woods von Neumann algebras and Factoriality

To any strongly continuous orthogonal representation of real line R on a real Hilbert space H , Hiai constructed q-deformed Araki-Woods von Neumann algebras for −1 < q <1, which are von Neumann algebras arising from non tracial representations of the q-commutation relations, the latter yielding an interpolation between Bosonic and Fermionic statistics. We settle that these von Neumann algebras are factors whenever dim(H ) ≥ 3 and completely determine their type. In the process we obtain and discuss ‘generator masas’ in these factors and establish that they are strongly mixing.

Date/Time

Venue

Seminar Hall

Speaker

Anoop V.P.

Affiliation

NISER

Title

To be announced

Date/Time

Venue

M4

Speaker

Nabin Kumar Jana

Affiliation

NISER, Bhubaneswar

Title

Radon-Nikodym theorem and conditioning

This is the second lecture on this topic with the following:Abstact: Radon-Nikodym theorem of measure theory was proved in 1930 and A. N. Kolmogorov laid the foundation of modern probability in 1933 where the formal played a crucial role. In this Short Lecture Series in Mathematics (SLSM), we discuss the conditioning of probability theory in the light of Radon-Nikodym theorem. Upon the interest of the audience, we may introduce the notion of martingals and their convergence theorems. We have scheduled these lectures in the F-slot of Thursday and planned to go in accordance with the pace of the audience. Basic understanding of measure theory and functional analysis will be the prerequisite.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Soumalya Joardar

Affiliation

JNCASR, Bangalore

Title

Weyl algebra, Hyperbolic space and Noncommutative Hyperbolic plane

Date/Time

Venue

SMS Seminar Hall

Speaker

Mr. Mithun Bhowmick

Affiliation

ISI Kolkata

Title

Theorems of Ingham, Levinson and Paley-Wiener on certain Lie groups

Abstract: In this talk, our focus will be on certain classical results due to Ingham, Levinson and Paley-Wiener which find optimal decay of the Fourier transform of nonzero functions vanishing on `large sets'. We will talk about these theorems in details and their generalizations on the $n$- dimensional Euclidean space, the $n$-dimensional torus and certain non-commutative Lie groups.

Date/Time

Venue

SMS Seminar Hall

Speaker

Rahul Kumar Singh

Affiliation

NISER

Title

Counting of rational planar curves in $ \mathbb{P}^3 $

Date/Time

Venue

SMS Seminar Room

Speaker

Kalyan Bidhan Sinha

Affiliation

JNCASR, Bangalore

Title

Introduction to unbounded operators

TBA

Date/Time

Venue

SMS Seminar Room

Speaker

Yasuyuki Kawahigashi

Affiliation

University of Tokyo

Title

Conformal field theory and operator algebras: lecture-4

I will present interactions among 2-dimensional conformal field theory, which is a kind of quantum field theory in physics, theory of operator algebras and the Moonshine conjecture which predicted mysterious relations between the finite simple group Monster and the elliptic modular function. I will emphasize representation theoretic aspects and do not assume anyknowledge of these theories.

Date/Time

Venue

Conference Room, School of Mathematical Sciences

Speaker

Dr. Anup Kumar Singh

Affiliation

IISER Berhampur

Title

Representation formulas for certain quadratic forms and a problem of constructing lifting maps between spaces of modular forms.

In this talk, we shall discuss the theta series associated with positive definite integral quadratic forms and some of its applications in getting formulas for the number of representations of positive integers by quadratic forms, using the theory of modular forms. The second part of this talk is about the construction of the Shimura and Shintani mappings between certain subspaces of modular forms of half-integral weights and integral weight respectively.

Date/Time

Venue

Online (Google Meet)

Speaker

Rimpa Nandi

Affiliation

SOA University, Bhubaneswar

Title

Castelnuovo-Mumford regularity and linear resolution property of ideals arising from graphs

Let $G$ be a simple finite graph with vertex set $V(G)=\{x_1,x_2,x_3,\dots,x_n\}$ and edge set $E(G)=\{e_1,e_2,e_3,\dots,e_q\}$. Also suppose that $I(G)$ is the edge ideal of $G$, where $I(G)=\langle x_{i}x_{j}~|~\{x_i,x_j\}\in E(G)\rangle$ $\subset R=K[x_1,x_2,\dots,x_n].$ We assume that $R(I(G))$ and $K[G]$ are the Rees algebra and toric algebra of $I(G)$ respectively.

In this talk we give a new upper bound for the regularity of edge ideals of gap-free graphs, in terms of their minimal triangulation. We also provide a new class of gap-free graphs such that $I(G)^s$ has linear resolution for $s\geq 3.$

We also show that if $G$ is connected and $R(I(G))$ is normal, then $\reg(R(I(G)))\leq \alpha_0(G)$, where $\alpha_0(G)$ is the vertex cover number of $G$. As a consequence, every normal K\"onig connected graph $G$, $reg(R(I(G))) = \mat(G)$, the matching number of $G$.

For a gap-free graph $G$, we give various combinatorial upper bounds for $\reg(R(I(G)))$. As a consequence we give various sufficient conditions for the equality of $\reg(R(I(G)))$ and $\mat(G)$. Finally we show that if $G$ is a chordal graph such that the toric algebra $K[G]$ has $q$-linear resolution$(q\geq 4)$, then $K[G]$ is a hypersurface, that is the defining ideal $I_G$ of $K[G]$ is generated by a single element, which proves the conjecture of Hibi-Matsuda-Tsuchiya affirmatively for chordal graphs.

Date/Time

Venue

Online

Speaker

Mr. Anantadulal Paul.

Affiliation

SMS, NISER

Title

Enumeration of singular curves with prescribed tangencies.

**Abstract**: The study of moduli spaces of stable maps and quantum cohomology theory plays a prominent role in modern enumerative geometry. A landmark result in this area is Kontsevich's recursion formula to enumerate rational curves in projective space. In the first part of this talk, we shall study a fiber bundle version of the above problem. We will consider the problem of enumerating rational curves in CP^3 whose image lies inside a CP^2 (which is also called a planar curve). We will show how Kontsevich's idea can be extended to the setting of fiber bundles.

In the second part of this talk, we will turn to classical enumerative geometry. We will study singular curves in a linear system that are tangent to a

given divisor. When the singularities are nodes, the question has been extensively studied by Caporaso and Harris. In this talk, we will give an approach to solve this question when the curve has more degenerate singularities. The method we will discuss comprises an explicit computation of the Euler class of an appropriate bundle. We then use excess intersection theory to compute the degenerate contribution to the Euler class.

Date/Time

Venue

LH-101

Speaker

Abhash Kumar Jha

Affiliation

NISER, Bhubaneswar

Title

Adjoint of some linear maps on the space of Jacobi cusp forms

Date/Time

Venue

PL-8

Speaker

Dr. Naraparaju Kishore Kumar

Affiliation

Birla Institute of Technology, Pilani

Title

Tensor Decompositions

Abstract: Tensor is a multidimensional array (for example matrix is a tensor of order 2). Tensors often arises from the discretizations of multidimensional functions that are involved in the numerical treatment of complex problems in many different areas of natural, financial or social sciences. The direct numerical treatment of these arrays leads to serious problems like memory requirements and the complexity of basic operations (they grow exponentially in d). In the last decade the approximation of multidimensional arrays has become a central issue in approximation theory and numerial analysis. The main idea of the approximation of a tensor is decomposing the given tensor as sums of outer products of vectors. In the language of functions, it is an approximation of multivariable functions by sums of products of univariate functions. Tensor decompositions has lot of applications in image processing, quantum chemistry, data mining, machine learning stochastic partial differential equations etc.In the matrix case (i.e tensor of order 2), the singular value decomposition (SVD) represents a matrix as sum of outer product of vectors. SVD algorithm requires O(n3) arithmeticoperations (if the matrix is of size n × n). So it is very expensive when the matrix dimensions are large. Various inexpensive techniques of low rank approximation based on skeleton/cross approximation are available in the literature. SVD and its applications, other low rank approximation techniques like RRQR, Interpolative decomposition, randomized algorithms, skeleton/cross approximation techniques will be discussed in the talk. Canonical,Tucker, Tensor Chain and Tensor Train formats for higher order tensors will be introduced.

Date/Time

Venue

M7

Speaker

Neeraj Kumar

Affiliation

Institute of Mathematical Sciences, Chennai

Title

Koszul algebras and Castelnuovo-Mumford regularity

Date/Time

Venue

SMS seminar room

Speaker

Shane D'Mello

Affiliation

IISER Pune

Title

Some results in the topology of real algebraic varieties

The topology of real algebraic varieties is the study of the topology of objects that can be defined real algebraically, particularly the restrictions that the real algebraic structure imposes on the topology. The main problem that motivated interest in this area is the so called Hilbert's sixteenth problem that was suggested by Hilbert in his famous address: to classify, up to isotopy, non-singular planar real algebraic curves of a given degree. Topologically, a non-singular real algebraic curve is merely the union of circles (in fact, the fixed point set a complex conjugation on a Riemann surface), and its isotopy class is simply determined by the arrangement of these circles with respect to each other. Nevertheless, a complete classification, which would mean identifying which of these arrangements can be realized as the zero set of a real polynomial in two variables of a given degree, has as yet only been successful up to degree 7. However, it has led to several tangential questions and generalizations, which we will discuss after a brief overview of the motivating problem.

Date/Time

Venue

SMS Seminar Room

Speaker

Nabin Kumar Jana

Affiliation

NISER, Bhubaneswar

Title

Radon-Nikodym theorem and conditioning

This is the *third lecture* on this topic with the following:

**Abstact:** Radon-Nikodym theorem of measure theory was proved in 1930 and A. N. Kolmogorov laid the foundation of modern probability in 1933 where the formal played a crucial role. In this Short Lecture Series in Mathematics (SLSM), we discuss the conditioning of probability theory in the light of Radon-Nikodym theorem. Upon the interest of the audience, we may introduce the notion of martingals and their convergence theorems. We have scheduled these lectures in the F-slot of Thursday and planned to go in accordance with the pace of the audience. Basic understanding of measure theory and functional analysis will be the prerequisite.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Pabitra Barik

Affiliation

IIT Madras

Title

Hitchin pairs on a singular curve

Date/Time

Venue

Seminar Room, SMS

Speaker

Mr. Bikramaditya Sahu

Affiliation

Ph.D. Student, SMS, NISER Bhubaneswar

Title

Blocking sets of certain line sets in PG(3,q)

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Pradeep Kumar Rai

Affiliation

IIT Patna

Title

Schur multiplier of some special p-groups

The Schur multiplier of a finite group is the second cohomology group with complex coefficients. It was introduced in the beginning of 20th century by Issai Schur in his work on projective representations. Since then they have been proved to be a powerful tool in group theory. To determine the Schur multiplier of a given finite group is often a difficult task. Therefore it is of interest to provide bounds for the numerical qualities such as the order, exponent and the rank of the Schur multiplier. In this talk we shall provide sharp lower and upper bounds for the order of some special p-groups and classify their covering groups.

Date/Time

Venue

Seminar Hall

Speaker

Sauvik Mukherjee

Affiliation

Presidency University, Kolkata,

Title

POISSON STRUCTURES ON CLOSED MANIFOLDS

Abstrat: We prove an h-principle for poisson structures on closed manifolds. Equivalently

we prove h-principle for symplectic foliation (singular) on closed manifolds. On open

manifolds however the singularities could be avoided and it is a known result by Fernandes

and Frejlich [1].

References

[1] Fernandes, Rui Loja; Frejlich, Pedro An h-principle for symplectic foliations. Int. Math. Res. Not. IMRN

2012, no. 7, 1505–1518. (Reviewer: David Iglesias Ponte)

Presidency University, Kolkata, India., e-mail:mukherjeesauvik@yahoo.com,

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Abhay Soman

Affiliation

ISI Bangalore

Title

On triviality of the reduced Whitehead group

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Fouzul Atik

Affiliation

SRM University

Title

On equitable partition of matrices and some problems related to graph theory

A partition of a square matrix A is said to be equitable if all the block of the partitioned matrix have constant row sums and each of the diagonal block is of square order. A *quotient matrix* Q of a square matrix A corresponding to an equitable partition is a matrix whose entries are the constat row sums of the corresponding blocks of A. A quotient matrix is an useful tool to find some eigenvalues of the matrix A. I will discuss some matrices whose eigenvalues are the eigenvalues of A and which are not the eigenvalues of a quotient matrix. Using this result we find eigenvalue localization theorems for matrices having an equitable partition. Finally, I will discuss some problems related to distance regular graph, Gersgorin disk theorem and distance matrix of graphs.

Date/Time

Venue

Online (GoogleMeet)

Speaker

Debangana Mukherjee

Affiliation

Montan University

Title

On fractional multi-singular Schrödinger operators

I will discuss about the nonlocal operators, in particular, the fractional Laplacian, and investigate the positivity properties of nonlocal Schrödinger type operators, driven by the fractional Laplacian by developing a criterion that links the positivity of the spectrum of such operators with the existence of certain positive supersolutions, thereby establishing necessary and sufficient conditions for the existence of a configuration of poles that ensures the positivity of the corresponding Schrödinger operator.

Date/Time

Venue

LH-104

Speaker

Dr. Safdar Quddus

Title

NONCOMMUTATIVE TOROIDAL $SL(2, \mathbb{Z})$ ORBIFOLD

Date/Time

Venue

TBA

Speaker

Subhamay Saha

Affiliation

The Technion – Israel Institute of Technology

An asymptotic framework for optimal control of multi-class stochastic processing networks, using formal diffusion approximations under suitable temporal and spatial scaling, by Brownian control problems (BCP) and their equivalent workload formulations (EWF), has beendeveloped by Harrison (1988). This framework has been implemented in many works for constructing asymptotically optimal control policies for a broad range of stochastic network models.To date all asymptotic optimality results for such networks correspond to settings where the solution of the EWF is a reflected Brownian motion in the positive orthant with normal reflections.In this work we consider a well studied stochastic network which is perhaps the simplest example of a model with more than one dimensional workload process. In the regime considered here, the singular control problem corresponding to the EWF does not have a simple form explicit solution,however by considering an associated free boundary problem one can give a representation for an optimal controlled process as a two dimensional reflected Brownian motion in a Lipschitz domain whose boundary is determined by the solution of the free boundary problem. Using the form of the optimal solution we propose a sequence of control policies, given in terms of suitable thresholds, for the scaled stochastic network control problems and prove that this sequence of policies is asymptotically optimal. As suggested by the solution of the EWF, the policy we propose requires a server to idle under certain conditions which are specified in terms of the thresholds determined from the free boundary. This is a joint work with A. Budhiraja and X. Liu.

Date/Time

Venue

SMS Seminar Room

Speaker

Dr. Anoop T. V.

Affiliation

IIT Madras

Title

On generalized Hardy-Sobolev inequalities

A brief history of classical Hardy inequalities and related results will be presented. Further, we talk about Generalized Hardy-Sobolev inequalities and its applications.

Date/Time

Venue

Mathematics Department Seminar Hall

Speaker

Ritwik Mukherjee

Affiliation

NISER

Title

Introduction to Smooth Manifolds

We will explain what is a differential k-form and define the De Rham Cohomology of a smooth manifold.

Date/Time

Venue

SMS Seminal Hall

Speaker

Samir Shukla

Affiliation

IIT Kanpur

Title

Connectedness of Certain Graph Coloring Complexes

Date/Time

Venue

Seminar hall

Speaker

Atibur Rahaman

Affiliation

NISER

Title

Partial dual construction for C*-Quantum groups

Given a Hopf algebra H in a braided category \mathcal{C} and a projection H\longrightarrow A to a Hopf subalgebra, one can construct a Hopf algebra r_{A}(H), called the partial dualization of H , with a projection to Hopf algebra dual to A. A non-degenerate Hopf pairing \omega :A\otimes B \longrightarrow 1 induces a braided equivalence between the Yetter-Drinfeld modules over a Hopf algebra and its partial dualization. In this seminar, we shall discuss this procedure in the general setting of C*-Quantum groups.

Reference:

1. Alexander Barvels, Simon Lentner, Christoph Schweigert, Partially dualized Hopf algebras have equivalent Yetter–Drinfel’d modules, Journal of Algebra 430 (2015) 303–342

2. Ralf Meyer, Sutanu Roy, Stanislaw Lech Woronowicz, Quantum group-twisted tensor products of C*-algebras II, J. Noncommut. Geom., 10 (2016), no. 3, 859-888.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Jyotishman Bhowmick

Affiliation

ISI Kolkata

Title

On the notions of connections and curvature in noncommutative geometry

One of the objectives of Noncommutative Geometry is to study operator algebras through differential geometric techniques. The geometric data associated to an operator algebra is a spectral triple. We will describe the construction of the space of forms coming from the spectral triple. Then we will discuss the question of existence and uniqueness of Levi-Civita connections for a spectral triple. Based on a joint work with D. Goswami and S. Joardar.

Date/Time

Venue

SMS seminar room

Speaker

Prof. Debashis Mondal

Affiliation

Oregon State University

Title

Markov random fields and geostatistics

Recent decades have witnessed significant growth and progress in spatial statistics, with applications in agriculture, epidemiology, geology, image analysis and other areas of environmental science. In recent years, new perspectives have emerged in connecting Gaussian Markov random fields with geostatistical models, and in advancing vast statistical computations. This series of lectures will focus on basic theory and computations of spatial statistics. Topics will include conditional and intrinsic autoregressions, connections between Markov random fields and geostatistics, variogram calculations, h-likelihood methods and matrix-free computations. Applications from agricultural variety trials, environmental sciences and geographical epidemiology will be discussed.

Date/Time

Venue

SMS Seminar Hall

Speaker

Professor B V Rao

Affiliation

CMI, Chennai

Title

Brownian Motion - Feynman's view

**Abstract:**Starting with the problem of heat equation witha potential and using Lie-Trotter product formula, Feynmanhas a heuristic way of explaining Brownian Motion.We shall discuss this. If time permits we shall discussWiener and Ito integrals.

Date/Time

Venue

SMS Seminar Hall

Speaker

Mr. Ranajit Goswami

Affiliation

NISER

Title

Spectral theorem for commutative C* algebras

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Kamalakshya Mahatab

Affiliation

University of Helsinki

Title

Application of The Resonance Method in Analytic Number Theory

In this talk we will briefly talk about the resonance method and some recent progress in the theory of the Riemann zeta function. We will also see some new results on Hardy's Z function, Argument of the Riemann Zeta function, Dirichlet L- functions, Divisor problem and Circle problem as applications of the resonance method. These results have appeared (and some works are under progress) in different manuscripts due to the speaker and coauthors.

Date/Time

Venue

Online (Google Meet)

Speaker

Anindya Ghatak

Affiliation

ISI Bangalore

Title

CP maps, Dilation and its applciations

Attached file

Date/Time

Venue

LH-101

Speaker

Gaurish Korpal

Affiliation

NISER, Bhubaneswar

Title

Celebrating 110th birthday of D. R. Kaprekar

**Abstract:** Dattarya Ramchandra Kaprekar was an Indian recreational mathematician who described several classes of natural numbers. The motive of this talk is to give a flavor of Elementary Number Theory and Iterations, by discussing the contributions of D. R. Kaprekar. I will discuss Kaprekar Numbers, Kaprekar Routines and Kaprekar Sequences. Nothing more than class 10 mathematics is needed to understand this talk.

Date/Time

Venue

LH-4

Speaker

Dr. Anupam Singh

Affiliation

IISER, Pune

- Title: Gaussian Elimination in classical groups
- Abstract: The classical row-column operations provide an efficient algorithm to solve word problem in the matrix group GL(n,k). We will see an analogues result for orthogonal and symplectic groups too.

Date/Time

Venue

Mathematics Seminar Room

Speaker

Alladi Sitaram

Affiliation

ISI, Bangalore

Title

The importance of Complex Analysis-1

Date/Time

Venue

Seminar Hall, SMS

Speaker

Sujeet Kumar Singh

Affiliation

NISER

Title

Modular forms and Sturm bounds

Date/Time

Venue

SMS Seminal Hall

Speaker

Arvind Kumar

Affiliation

HRI, Allahabad

Title

Rankin-Cohen brackets and identities among eigenforms

Date/Time

Venue

SMS seminar room

Speaker

Ramprasad Kale

Affiliation

4th Year student, SMS, NISER

Title

Some Topics in Sequential Estimation

Confidence intervals constructed from a fixed-sample size procedure may sometimes be too wide to be of any practical use. Hence, to avoid such a problem, it is desirable to construct confidence intervals with fixed-width. G. B. Dantzig (1940) showed that there did not exist any fixed sample size procedure which produces fixed-width confidence interval with a prescribed confidence level. Charles Stein (1945, 1949) introduced the groundbreaking idea of sampling in two stages to construct fixed-width confidence intervals with a prescribed confidence level. In this talk, we consider the problem of fixed-width interval estimation of normal mean with unknown variance. In doing so, we develop Stein’s two-stage procedure and successively go through its modifications leading to modified two stage and purely sequential procedures. We also discuss properties associated with these procedures and how they compare with each other. If time permits we will also consider the problem of fixed-width interval estimation of a p dimensional normal mean vector with a certain structure for the dispersion matrix.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Andrey Krutov

Affiliation

Independent University of Moscow

Title

Jet Spaces

We will discuss jet spaces and symmetries of partial differential equations.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Kunal Krishna Mukherjee

Affiliation

IIT Madras

Title

Some recent results on non commutative dynamics

I will survey some recent results on actions of groups on von Neumann algebras, the emphasis being on joinings and spectral properties.

Date/Time

Venue

SMS seminar room

Speaker

Chiranjit ray

Affiliation

IIT G

Title

Arithmetic properties of certain partition functions and modular forms

Abstract: In this talk, we will discuss some arithmetic and distribution type results on various partition functions, namely, Andrews’ singular overpartitions, cubic and overcubic partition pairs, and Andrews’ integer partitions with even parts below odd parts. We use some dissection formulas of Ramanujan’s theta functions, and arithmetic properties of modular forms and eta-quotients to study the distributions and to find some infinite family congruences of these partition functions. Also, using Radu’s algorithm on modular forms, we prove a conjecture on cubic partition pairs.

Date/Time

Venue

SMS Seminar Hall

Speaker

Mr. Sanjay Mukherjee

Affiliation

NISER

Title

Counting the number of spanning trees of graphs

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Mr. Archisman Bhattacharjee

Affiliation

SMS, NISER

Title

A proof of Horrocks' Theorem

* Abstract:* Horrocks' Theorem is an indispensable tool to prove Quillen-Suslin Theorem, which gives a sufficient condition for finitely generated projective modules to be free. In this talk, we will talk about a version of Horrocks' Theorem which uses concepts of completable unimodular rows over a ring. First, we will prove the theorem for local rings, then generalize it using the Local-Global Principle.

Date/Time

Venue

Online

Speaker

Mr. Sayan Gupta

Affiliation

SMS, NISER

Title

Random Graph.

**Abstract:** In this talk we will describe Random Graph through two models, 'Binomial Random Graph' and 'Erdos-Rényi' random graph. We will describe some of their properties and the relation between them. Further we will discuss threshold function of a graph property and how graph properties vary as the number of edges of a random graph increases.

Date/Time

Venue

LH-101

Speaker

Dr. Sudeshna Basu

Affiliation

George Washington University, USA

Title

Stability of ball properties in Banach spaces

Date/Time

Venue

M1

Speaker

Professor Rahul Roy

Affiliation

Indian Statistical Institute, New Delhi

Title

Rank of random matrices

Date/Time

Venue

SMS seminar hall

Speaker

Pratyusha Chattopadhyay

Affiliation

Indian Statistical Institute - Bangalore

Title

Relation between orbit spaces of unimodular elements and its application

This is a topic in classical algebraic K-Theory. I will recall definitions of elementary linear group, elementary symplectic group, linear transvection group, symplectic transvection group and symplectic group w.r.t. any alternating form. These groups have natural action on the set of unimodular elements. I will briefly discuss how bijections between orbit spaces of unimodular elements under different group actions are established. Finally, I will talk about an application of these results, namely improving injective stability bound for K1 group.

Date/Time

Venue

Seminar Room, SMS

Speaker

Professor Y. Martin

Affiliation

Universidad de Chile, Santiago

Title

On an integral kernel for twisted Koecher-Maass series associated to Siegel cusp forms of degree two

We give an explicit formula for the integral kernel of the twistedKoecher-Maass series associated to a degree two Siegel cusp form F, where the twist is realized by any Maass waveform whose eigenvalue is in the continuum spectrum. From such a kernel we deduce the analytic properties of those twisted Koecher-Maassseries, and show how the later can be expressed in terms of Dirichlet series associated to the Fourier-Jacobi coefficients of $F$.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Ami Viselter

Affiliation

University of Haifa, Israel

Title

Around Property (T) for Quantum Groups

Date/Time

Venue

Seminar Hall, SMS

Speaker

Santu Pal

Affiliation

SMS, NISER

Title

Cryptanalysis of stream cipher

Abstract: Stream cipher plays an important role in cryptography. The basic component of stream cipher is Linear Feedback Shift Registrar. Here we will discuss about the general construction of a LFSR based stream cipher and the cryptanalysis of stream cipher.

Date/Time

Venue

M1

Speaker

Nilkantha Das

Affiliation

SMS, NISER

Title

Counting nodal curves with prescribed tangencies

In this talk, we will prove Caporaso-Harris formula for counting plan curves of any genus. This formula gives the answer of the following problem:How many degree d curves are there in CP2 having δ nodes and passing through d(d+3)/2 − δ generic points?

Date/Time

Venue

SMS Seminar Hall

Speaker

Dr. Mukesh Kumar Nagar

Affiliation

IIT Dharwad

Title

Immanants of Laplacians of Trees

Date/Time

Venue

Mathematics Seminar Room

Speaker

TSSRK Rao

Affiliation

ISI, Bangalore

Title

APPROXIMATE BIRKHOFF-JAMES ORTHOGONALITY

**Abstract: **We discuss approximate Birkhoff-James orthogonality of bounded linear operators defined between normed linear spaces X and Y. As an application of the results obtained, we characterize smoothness of a bounded linear operator T under the condition that K(X, Y), the space of compact linear operators is an M−ideal in L(X,Y), the space of bounded linear operators.

Date/Time

Venue

SMS conference Hall

Speaker

Mr. Rajeeb Ranjan Mohanta

Affiliation

NISER Ph.D Student

Title

Ultracontractivity in mixed q-deformed Araki-Woods von Neumann algebras

In this talk we will first discuss about the non-commutative Lp spaces and recall the construction of the mixed q-deformed Araki-Woods von Neumann algebras. Then we will define the Ornstein-Uhlenbeck semigroups for this von Neumann algebra and study their ultracontractivity.

Date/Time

Venue

Online

Speaker

Devashish Sonowal

Affiliation

SMS, NISER

Title

Taylor's theorem from the viewpoint of heat equation

Abstract: Employing solution of heat equation, we prove Taylor's theorem with Peano form of the remainder. In addition, we derive the Taylor series of an infinitely differentiable function under the additional assumption that the n'th derivative does not grow faster than the n'th power of some fixed positive constant.

**Googlemeets link**: https://meet.google.com/pdg-ymra-wkv

All are cordially invited.

Date/Time

Venue

Online

Speaker

Mr. Aanjaneya Rath

Affiliation

SMS, NISER

Title

Complex Tori

**Abstract:** The goal of the talk is to study complex tori and see some of its properties .We will begin with defining what a complex tori is and show that it is a complex manifold. Then we will classify complex tori of dimension one and show that each such tori is an elliptic curve.

Date/Time

Venue

LH-101

Speaker

S Bibek Sankar

Affiliation

NISER, Bhubaneswar

Title

Exploring Chaos

**Abstract:** In this talk, we try to understand elements of chaos theory in dynamical systems numerically and graphically. We also try to understand the the various properties like period doubling and chaos of the famous Logistic Map. Along with it some other less known maps, the Tent Map and the Gauss Map will also be analyzed. In particular Gauss Map shows very interesting properties like coexisting attractors and reverse period doubling.The principal aim is to explore the deep relationship among dynamical systems, chaos and fractals, and to uncover structure even when order seems to be absent.Prerequisite :Mathematical Background till class 12.

Date/Time

Venue

LH 101

Speaker

Dr. Amit Tripathi

Affiliation

Indian Statistical Institute, Bangalore

Title

VECTOR BUNDLES AND GEOMETRY OF HYPERSURFACES

Let S ⊂ CP 3 be ’almost any’ projective surface of degree ≥ 4. ClassicalNoether-Lefschetz theorem states that any curve C ⊂ S can be written as an intersectionC = S∩ S 0 where S 0 is some surface in CP 3. Grothendieck-Lefschetz theorem generalizesthis result for higher dimension.In this survey talk we will discuss these theorems and the corresponding results forvector bundles. We will study related aspects of vector bundles over hypersurfaces andcomplex projective spaces. Our emphasis will be on extendibility theorems and varioussplitting criterion for vector bundles.We will also mention some recent results and open problems. The talk should beaccessible to a graduate student.

Date/Time

Venue

conference room

Speaker

Subhamay Saha

Affiliation

Technion-Israel Institute of Technology

Title

TBA

TBA

Date/Time

Venue

Seminar Room, SMS

Speaker

Dr. Anirban Mukhopadhyay

Affiliation

IMSc. Chennai

Title

Distribution of Primes

In this lectures, we would discuss probabilistic model of primes leading to heuristics about their distribution. We would see many surprising irregularities popping up alongside expected results. A survey of several recent and important results would be presented in a way accessible to non-experts.

Date/Time

Venue

LH-5

Speaker

Professor S. Kumaresan

Affiliation

University of Hyderabad

Title

TBA

This talk will be in elementary level and first year Integrated MSc students should attained it.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Ami Viselter

Affiliation

University of Haifa, Israel

Title

Locally compact quantum groups: the von Neumann algebraic approach-4

Lecture series abstract: We will survey the von Neumann algebraic approach to locally compact quantum groups in the sense of Kustermans and Vaes, roughly following the treatment by Van Daele. We will begin with an intro to the theory of weights of von Neumann algebras. We will then proceed to describe locally compact quantum groups. If there is any time left, we will present some recent progress in the field. The prerequisite for attending the talks is some basic knowledge of C*-algebras (and perhaps also von Neumann algebras, depending on the audience).

Date/Time

Venue

SMS seminar room

Speaker

Manas Kar

Affiliation

National Taiwan University in Taiwan

Title

Inverse problems for reconstructing inclusion and identifying unknown parameter

In general, inverse problems are those where one needs to recover the unknown parameter of a system from the knowledge of the external observation. In this talk, I will mainly give an overview of Calder\'on’s inverse problems arising in several linear and nonlinear partial differential equations. I will discuss two different kinds of inverse problems for the Maxwell system and p-Laplace equation. One is the parameter identification problems and another one is the shape reconstruction issues. In particular, I will concentrate on the problem of determining the conductivity of a medium and the shape of an inclusion from the knowledge of boundary voltage or current measurements.

Date/Time

Venue

SMS Seminar Hall

Speaker

Nabin Kumar Meher

Affiliation

HRI

Title

Borel conjecture on normal number

Abstract: In this talk, we define normal number and state Borel conjecture. In 1973, Mahler first proved a result towards Borel conjecture. Here, we discuss a conditional quantitative version of Mahler result.

Date/Time

Venue

M1/M4

Speaker

Prof. N. S. N. Sastry

Affiliation

IIT Dharwad

Title

Finite Simple Groups

Abstract: This will be an introductory talk towards the theory of finite simple groups and their corresponding geometries. We shall discuss some examples which will be accessible to master level students.

Date/Time

Venue

SMS Seminar Hall

Speaker

Mr. Gorekh Prasad Sena

Affiliation

PhD Student, NISER

Title

Integral Points on Curves

Date/Time

Venue

sms seminar hall

Speaker

Suman Mukherjee

Affiliation

NISER

Title

Hardy Littlewood Maximal Function and it's applications

Date/Time

Venue

Online (Google Meet)

Speaker

Anshu

Affiliation

IISER Bhopal

Title

Homotopical Stable Ranks of $\mathrm{C}^*$-algebras

In the first part of the talk, we will define the connected stable rank and general stable rank. We will then discuss some basic examples and properties of these ranks. We will also discuss the relationship between the homotopical stable ranks of a $\mathrm{C}^*$-algebra $A$ and its $K$-theory. Then we will move on to give brief descriptions of a $C(X)$-algebra and a crossed product $\mathrm{C}^*$-algebra by a finite group. In the later part of the talk, we will provide estimates of the connected stable rank for upper semicontinuous $C(X)$-algebras and crossed product $\mathrm{C}^*$-algebras by finite groups. We will talk about a condition on the finite group actions, which is called the Rokhlin property. We will also prove that if $A$ has any of the homotopical stable rank one, then the crossed product $\mathrm{C}^*$-algebra by an action with the Rokhlin property also has the corresponding homotopical stable rank one.

Date/Time

Venue

Vertual

Speaker

NKU Sarada Anoushka

Affiliation

NISER

Title

State spaces of partially ordered abelian groups with an order unit

**Abstract**: We will talk about states and state spaces of partially ordered abelian groups with an order unit. A state on a partially ordered abelian group with order unit (G,u) is a positive homomorphism (a group homomorphism that takes positive elements to positive elements) from G to the real numbers with natural ordering such that u is mapped to 1. We will also see state spaces in general, i.e., we will talk about the collection of all states on (G,u) and will try to see the effects on the state space of changing the order unit.

Friday, November 26 · 4:00 – 5:00pm

Google Meet joining info

Video call link: https://meet.google.com/sht-xuxz-qnk

Or dial: (US) +1 724-617-2011 PIN: 431 647 541#

Date/Time

Venue

LH-101

Speaker

Dr. Ghurumuruhan Ganesan

Affiliation

EPFL, Lausanne

Title

Infection Spread and Stability in Random Graphs

Date/Time

Venue

LH-301

Speaker

Dr. Safdar Quddus

Affiliation

NISER, Bhubaneswar

Title

Ultrafilters of $\mathbb N$ and functionals on $\mathbb D(l_2)$

Date/Time

Venue

M5

Speaker

Rajesh Kannan

Affiliation

Univeristy of Manitoba

Title

Nonnegative tensors and their applications

An $m$-order $n$-dimensional square real tensor $\mathcal{A}$ is a multidimensional array of $n^m$ elements of the form$\mathcal{A} = (A_{i_1\dots i_m})$, $A_{i_1\dots i_m} \in \mathbb{R}$, $1 \leq i_1, \dots , i_m \leq n.$ (A square matrix of order $n$ is a $2$-order $n$-dimensional square tensor.) An $m$-order $n$-dimensional square real tensor is said to be a nonnegative (positive) tensor if all its entries are nonnegative (positive). We shall discuss the Perron-Frobenius theory for nonnegative tensors. Using these results we establish a sufficient condition for the positive semidefiniteness of homogenous multivariable polynomials.

Date/Time

Venue

SMS seminar hall

Speaker

Ananya Lahiri

Affiliation

Chennai Mathematical Institute

Title

On two dimensional polynomial phase signal parameter estimation

Abstract: Two dimensional polynomial phase signal has uses in modeling black and white texture. We will discuss how to estimate the parameters of the model from observed data set and about the large sample properties of these estimators.

Date/Time

Venue

SMS Seminar Hall

Speaker

Prof. Bart De Bruyn

Affiliation

Ghent University, Belgium

Title

Finite Fields

This will be the second lecture of a series of five on Finite Fields.

Date/Time

Venue

SMS Seminar Room

Speaker

Antar Bandyopadhyay

Affiliation

Indian Statistical Institute, New Delhi

Title

Random Graphs (4th Lecture)

**This is a Short Lecture Series in Mathematics (SLSM) consisting of 4 lectures of 90 minutes each. This is the final lecture in this series.**

**Abstract:** The first half of the mini course will be an introducing to the two classical models of random graphs (a.k.a. Erdős-Rényi random graphs) and discuss the phenomenon of phase transition. We will also discuss thresholds for monotonic properties with examples including connectivity threshold and sub-graph containment threshold.

In the second half of the course we will consider other kind of random graphs. In particular, we will discuss various models for complex networks, including Albert-Barabási preferential attachment models. We will discuss "scale-freeness", asymptotic degree distribution and "small-world phenomenon". Properties of super and sub-linear preferential attachment models and some recent developments in de-preferential attachment models will also be discussed.

If time permits we will also introduce the random geometric graphs and discuss asymptotic of the connectivity threshold.

Date/Time

Venue

SMS Seminar Hall

Speaker

Deepika

Affiliation

IIT Kanpur

Title

Approximation Property and Its Variants in Weighted Spaces of Holomorphic Functions on Banach Spaces

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Jyoti Prakash Saha

Affiliation

Ben-Gurion University

Title

Purity for families of Galois representations

Date/Time

Venue

Mathematics Seminar Room

Speaker

Sudeshna Basu

Affiliation

George Washington University, USA

Title

Linear Hahn Banach Extension of module homomorphisms in Hilbert and Banach modules

The notion of linear Hahn-Banach extension operator was first studied in detail by Heinrich and Mankiewicz (1982). Previously, J. Lindenstrauss (1966) studied similar versions of this notion in the context of non separable reflexive Banach spaces. Subsequently, Sims and Yost (1989) proved the existence of linear Hahn-Banach extension operators via interspersing subspaces in a purely Banach space theoretic set up. In this paper, we study similar questions in the context of Banach modules and module homomorphisms, in particular, Banach algebras of operators on Banach spaces. Based on Dales, Kania, Kochanek, Kozmider and Laustsen(2013), and also Kania and Laustsen (2017), we give complete answers for reflexive Banach spaces and the non-reflexive space constructed by Kania and Laustsen from the celebrated Argyros-Haydon's space with few operators.

Date/Time

Venue

M1

Speaker

G. Priyanga

Affiliation

Texas A & M University, USA

Title

Factorization of Identity map through large diagonal operators

Date/Time

Venue

SMS Seminar Room

Speaker

Yasuyuki Kawahigashi

Affiliation

University of Tokyo

Title

Conformal field theory and operator algebras: lecture-2

I will present interactions among 2-dimensional conformal field theory, which is a kind of quantum field theory in physics, theory of operator algebras and the Moonshine conjecture which predicted mysterious relations between the finite simple group Monster and the elliptic modular function. I will emphasize representation theoretic aspects and do not assume anyknowledge of these theories.

Date/Time

Venue

Conference Room, School of Mathematical Sciences

Speaker

Dr. Manish Singh

Affiliation

TIFR Centre for Applicable Mathematics

Title

Structure theorems for balance laws

In this talk, I will present Lax-Oleinik type explicit formulafor the solution of some balance laws and discuss its Structure Theory.

Date/Time

Venue

Online (Google Meet)

Speaker

Veekesh Kumar

Affiliation

IMSc, Chennai

Title

On inhomogeneous extension of Thue-Roth's type inequality with moving targets

Let $\Gamma\subset \overline{\mathbb Q}^{\times}$ be a

finitely generated multiplicative group of algebraic numbers. Let

$\delta, \beta\in\overline{\mathbb Q}^\times$ be algebraic numbers

with $\beta$ irrational. In this talk, I will prove that there

exist only finitely many triples $(u, q, p)\in\Gamma\times\mathbb{Z}^2$

with $d = [\mathbb{Q}(u):\mathbb{Q}]$ such that

$$

0<|\delta qu+\beta-p|<\frac{1}{H^\vareps

$$

where $H(u)$ denotes the absolute Weil height. As an application of

this result, we also prove a transcendence result, which states as

follows: Let $\alpha>1$ be a real number. Let $\beta$ be an algebraic

irrational and $\lambda$ be a non-zero real algebraic number. For a

given real number $\varepsilon >0$, if there are infinitely many

natural numbers $n$ for which $||\lambda\alpha^n+\beta|| < 2^{-

\varepsilon n}$ holds true, then $\alpha$ is transcendental, where

$||x||$ denotes the distance from its nearest integer.

**Google Meet Link: **meet.google.com/rpj-qpwn-ows

Date/Time

Venue

Online (via Google Meet)

Speaker

Gourav Kumar Meher

Affiliation

NISER

Title

Inverse problems and Tikhonov regularization

Date/Time

Venue

LH301

Speaker

Dr. Suchismita Das

Title

How to measure uncertainty in the weighted lifetime distribution

Every probability distribution has some uncertainty associated with it. The concept of Shannon’s entropy provide a quantitative measure of this uncertainty. But for some probability distributions the Shannon’s entropy measure may be negative and then it is no longer an uncertainty measure. To overcome this problem the concept of generalized entropy has been introduced in literature. In many practical situations it has been seen that when an investigator collect a sample of observations produced by nature, according to a certain model, the original distribution may not be reproduced due to various reason. For this reason it is important to consider the concept of weighted distribution. Motivated with the usefulness of the generalized entropy and the weighted lifetime distributions, we introduce the concept of weighted generalized entropy and discuss several properties of this model.

Date/Time

Venue

PL-8

Speaker

Dr. Swapnil Lokhande

Affiliation

Indian Statistical Institute, Kolkata

Title

Integer solutions of $Y^3=X^2+k$

Date/Time

Venue

SMS conference room

Speaker

Shilpa Gondhali

Affiliation

University of Haifa

Title

Topology of quotients of the complex Stiefel manifold

Given a differentiable manifold $M$, understanding 'topology of $M$' means solving the Vector Field Problem on $M$, analyzing $K$ rings of $M$, immersion problem, etc. It is considered as a first step while analyzing the space completely. We will begin by explaining terms and an overview of the concept of topology of a manifold. We will consider actions of a finite cyclic group of order $m$ and the circle on the complex Stiefel manifold. Manifolds obtained as orbit spaces of these actions are called $m$-projective Stiefel manifold and right generalized complex projective Stiefel manifold respectively. We will discuss topology of these manifolds. (This is part of joint work with P. Sankaran and B. Subhash.)

Date/Time

Venue

Seminar Hall

Speaker

Arijit Dey

Affiliation

IIT Madras

Title

Moduli space of torsion free Sheaves over reducible singular curve

Date/Time

Venue

SMS Seminar Hall

Speaker

Prof. Bart De Bruyn

Affiliation

Ghent University, Belgium

Title

Finite Fields

This will be the last lecture of a series of five on Finite Fields.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Partha Sarathi Chakraborty

Affiliation

IMSc

Title

Instances of local index formula-II

Local Index formula is at the heart of the so called hard Riemannian aspects of Noncommutative Geometry. We will try to see why thisis so important. However so far we have only one computation of the local index formula. We will discuss two more computations.

Date/Time

Venue

SMS Seminar Room

Speaker

Anirvan Chakraborty

Affiliation

Ecole Polytechnique Federale de Lausanne, Switzerland

Title

Introduction to Functional Data Analysis

Functional Data Analysis is one of the frontline areas of research in statistics. The field has grown considerably mainly due to the plethora of data types that cannot be handled and analyzed by using conventional multivariate statistical techniques. Such data are very common in areas of meteorology, chemometrics, biomedical sciences, linguistics, finance etc .The lecture series will primarily aim at introducing the field of functional data analysis. Since functional data analysis is broadly defined as the statistical analysis of data, which are in the form of curves or functions, we will start with probability distributions and random elements in infinite dimensional Hilbert spaces, concepts of mean and covariance kernel/operator, the associated Karhunen-Loeve expansion and some standard limit theorems in Hilbert spaces. We will then discuss some selected statistical inference problems involving functional data like inference for mean and covariance operators, functional principal component analysis, functional linear models, classification problem with functional data, robust inference techniques for functional data etc. We will recall some results from functional analysis as and when required during the lectures.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Shreedevi K. Masuti

Affiliation

Chennai Mathematical Institute

Title

Hilbert functions of Gorenstein K-algebras

Gorenstein rings are very common and significant in many areas of mathematics. The classification, up to analytic isomorphism, of Gorenstein local K-algebras plays an important role in commutative algebra and algebraic geometry. The problem is difficult even if we restrict the K-algebras to the Artinian. One of the most significant information on the structure of K-algebra is given by its Hilbert function. Recently, jointly with M. E. Rossi, we characterized the Hilbert functions of Gorenstein K-algebras in some cases (K-algebras of socle degree 4). In this talk, we will discuss this new development.

Date/Time

Venue

sms seminar hall

Speaker

Dr. Pervez Sarwar

Affiliation

ISI Kolkata

Title

Algebraic K-theory and homology stability

Abstract: We shall begin with the homotopy invariance property of K-theory.After reviewing monoids and monoid algebras, we present some results which aremonoid version of the homotopy invariance property in K-theory. This answers a question ofGubeladze. Next, we will discuss the monoid version of Weibel's vanishing conjectureand some results in this direction. Finally, we will talk about the homology stability for groups.Here we present a result which improves homology stability for symplectic groups.If the time permits, some application of the homology stability will be given to the hermitian K-theory.

Date/Time

Venue

SMS Seminar Room

Speaker

Suratno Basu

Affiliation

IMSc Chennai

Title

Degeneration of intermediate Jacobians and the Torelli type theorems

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Sazzad Ali Biswas

Affiliation

University of Copenhagen

Title

Non-abelian local root numbers and the Langlands' lambda functions

In his Ph.D thesis, John Tate attached local root numbers with characters of a non-Archimedean local field of characteristic zero. Robert Langlands (later P. Deligne ) proved the existence theorem of non-abelian local root numbers of higher dimensional complex local Galois representations. The local Langlands correspondence preserves thisroot numbers and the global root number is a product of local root numbers. So the explicit computation of the local root numbersis an integral part of the Langlands programs. But for arbitrary higher dimensional Galois representations we do not have any explicit formula for the local root numbers. To give an explicit formula of the local root number of an induced representation of a local Galois group of a non-Archimedean local field F ofcharacteristic zero, first we have to compute the Langlands' lambda function \lambda_{K/F} for a finite extension K/F . The plan of the talk is as follows:

- Review of local and global root numbers
- To explain the computations of the local root numbers for a particular local Galois representations (e.g. Heisenberg representations)
- And the computation of the lambda function \lambda_{K/F} except when K/F is quadratic wildly ramified extensions
- If time permits, then I will explain some of my ongoing projects regarding root numbers and some open problems.

Date/Time

Venue

Online (GoogleMeet)

Speaker

G Arunkumar

Affiliation

IISc Bangalore

Title

Quasi-Dynkin diagram and the root multiplicities of Borcherds-Kac-Moody Lie (super)algebras

This talk is divided into two parts: Let g be a Borcherds-Kac-Moody-Lie (super)algebra with the associated Quasi-Dynkin diagram G. In the first part, I will prove that the generalized chromatic polynomial of the graph G can be recovered from the Weyl denominator identity of g. From this result, I will deduce a closed formula for certain root multiplicities of g. Also, we construct a basis for these root spaces of g. In the second part, we are interested in the chromatic symmetric function of the graph G. I will prove an expression for the chromatic symmetric function of G in terms of root multiplicities of g. As an application, we will see Lie theoretic proof of many results of Stanley on chromatic symmetric functions. Stanley's tree conjecture is an important conjecture in the theory of chromatic symmetric functions which states that non-isomorphic trees are distinguished by their chromatic symmetric functions. We propose a Lie theoretic method to approach this conjecture. Finally, I will briefly discuss some future directions.

Date/Time

Venue

LH 101

Speaker

Professor Debasis Kundu

Affiliation

Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur

Title

A Journey Beyond Normality

Abstract: Normal distribution has been used quite extensively in different areas of science and technology both in theory and practice. Although, it has several desirable properties, it has its own limitations also. Recently, various non-normal distributions (both univariate as well as multivariate) have been proposed in the literature for data analysis purposes. In this talk, we will consider different non-normal distributions and discuss their properties and provide applications in different areas.

Date/Time

Venue

To be announced

Speaker

Mr. Bikramaditya Sahu

Affiliation

NISER, Bhubaneswar

Title

Minimal blocking sets in PG(2,q)

Abstract: In this talk we will review on the minimal blocking sets of external, tangent and secant lines to an irreducible conic in PG(2,q).

Date/Time

Venue

Seminar Room, SMS

Speaker

Professor Ravi S. Kulkarni

Affiliation

Bhaskaracharya Pratisthan, Pune

Title

Symmetry, A Mathematician's Perspective

Date/Time

Venue

Seminar Room, Mathematics Department

Speaker

Deepika Kumari

Affiliation

Guru Gobind Singh Indraprastha University, Delhi

Title

Introduction to the Chen's biharmonic conjecture

In my presentation, I will give some brief introduction to biharmonic submanifold. Also, I will introduce the Chen's conjecture of biharmonic submanifold and present some recent developments of conjecture.

Date/Time

Venue

M4

Speaker

Prof. S. Krishnan

Affiliation

IIT Bombay

Title

Hook Immanantal and Hadamard inequalities for q-Laplacians of trees

Date/Time

Venue

SMS SEMINAR HALL

Speaker

Dr. Kunal Krishna Mukherjee

Affiliation

IIT Madras

Title

On dynamical system preserving weights

Date/Time

Venue

SMS Seminar Room

Speaker

Tulasi Ram Reddy

Affiliation

NYU, Abu Dhabi

Title

Zeros of random polynomials

Abstract: In this talk I will briefly introduce the study of random polynomials. I will provide a brief survey of some results. Further we will focus on the study critical points (zeros of derivative) in relation to the zeros of random polynomials, initiated by Pemantle and Rivin. It can be seen from the simulations that the zeros closely pair with the critical points and we investigate this phenomenon. We also establish similar phenomenon for zeros of higher derivatives. Further we attempt to compute the pairing distance between zeros and critical points of random polynomials. We will discuss the problem in the case when all the zeros of the polynomial are real. I will also pose some questions of interest and connections to other well known problems.

Date/Time

Venue

SMS seminar room

Speaker

Prof. Debashis Mondal

Affiliation

Oregon State University

Title

Introduction to spatial statistics

Recent decades have witnessed significant growth and progress in spatial statistics, with applications in agriculture, epidemiology, geology, image analysis and other areas of environmental science. In recent years, new perspectives have emerged in connecting Gaussian Markov random fields with geostatistical models, and in advancing vast statistical computations. This series of lectures will focus on basic theory and computations of spatial statistics. Topics will include conditional and intrinsic autoregressions, connections between Markov random fields and geostatistics, variogram calculations, h-likelihood methods and matrix-free computations. Applications from agricultural variety trials, environmental sciences and geographical epidemiology will be discussed.

Date/Time

Venue

Seminar Hall

Speaker

Dr. Krishanu Dan

Affiliation

CMI, Chennai

Title

Secant Bundles on Symmetric Power of Curves.

Abstract: Let $C$ be a smooth, projective, irreducible curve over the

field of complex numbers, and $C^n$ denotes the $n$-fold Cartesian

product of $C$. The symmetric group of $n$ elements acts on $C^n$ and

let $S^n(C)$ be the quotient. This is a smooth, irreducible, projective

variety of dimension $n$, called the $n$-th symmetric power of $C$.

Given a vector bundle $E$ of rank $r$ on $C$, one can naturally

associate a rank $nr$ vector bundle on $S^n(C)$, called the $n$-th

secant bundle of $E$. In this talk, we will discuss stability conditions

of secant bundles on $S^n(C)$.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Parangama Sarkar

Affiliation

Chennai Mathematical Institute

Title

Mixed Multiplicities and Rees’ theorem for filtrations

In this talk I will discuss mixed multiplicities of (not necessarily Noetherian) filtrations of m-primary ideals in a Noetherian local ring (R, m). I will give the construction of a real polynomial whose coefficients give the mixed multiplicities generalizing the classical theory for m-primary ideals. As a consequence, I will show that a classical theorem due to Rees, holds true for (not necessarily Noetherian) filtrations. I will also discuss a result which deals with non m-primary and non-Noetherian filtrations of ideals and partially generalizes another theorem of Rees.

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Eshita Mazumdar

Affiliation

ISI Bangalore

Title

Two Extremal Problems on Set Addition

Typically an extremal problem deals with the problem of estimating the maximum or mini- mum possible cardinality of a collection of finite objects that satisfies certain requirements. In my talk I am going to present my most recent research works related to extremal problems. For a finite abelian group G and A ⊂ [1, exp(G) − 1], the A-weighted Davenport Constant DA(G) is defined to be the least positive integer k such that any sequence S with length k over G has a non-empty A-weighted zero-sum subsequence. The original motivation for introducing Daven- port Constant was to study the problem of non-unique factorization domain over number fields. The precise value of this invariant for any group and for any set A is still unknown. In first half of my talk, I will present an Extremal Problem related to Weighted Davenport Constant, which we introduced and discuss several exciting results for any finite abelian group. It is a joint work with Prof. Niranjan Balachandran. In second part of my talk, I will discuss how to improve the Plu ̈nnecke inequality for iterated sumsets over any abelian group G. While doing so we estab- lished a bridge between almost a century old Macaulay’s theorem in commutative algebra and iterated sumsets in additive combinatorics. This process leads us to define an extremal problem as well. This is a joint work with Prof. Shalom Eliahou.

Date/Time

Venue

Online (GoogleMeet)

Speaker

Arunava Mandal

Affiliation

IISER Mohali

Title

The structure of Cartan subgroups in Lie groups and Power maps

Cartan subgroups of Lie groups play a crucial role in the study of the structure of Lie groups, the behavior of the power maps, and also in determining whether the exponential map is surjective or has a dense image. Here we present some recent progress on `the density/surjectivity of the power maps of Lie groups ', and `the structural aspects of Cartan subgroups' and its applications on the characterization of the density of the power map in Lie groups.

Date/Time

Venue

LH 101

Speaker

Dr. Sarath Sasi

Title

Weighted Eigenvalue Problem in the Exterior Domain

We consider a weighted quasilinear eigenvalue problem in the exterior domain. We establish the existence of a positive principal eigenvalue and discuss the regularity and the asymptotic behaviour at infinity of the first eigenfunctions. A local and the global antimaximum principle is also presented.

Date/Time

Venue

LH 4

Speaker

Sneh Bala Sinha

Affiliation

Harish Chandra Research Institute

In this talk, I will discuss an infinite family of numbers involving Briggs-Euler- Lehmer constants, Euler’s constant and linear forms of logarithms of non-zero algebraic numbers. I will show that these infinite family of numbers are transcendental with at most one exception. This result generalizes a recent result of Murty and Zaytseva.

Date/Time

Venue

SMS seminar Hall

Speaker

Ajay Singh Thakur

Affiliation

Indian Statistical Institute, Bangalore.

Title

A CONSTRUCTION OF NON-KAHLER COMPLEX MANIFOLDS

The compact torus S1 × S1 has a structure of Riemann surfaceand therefore is a complex projective manifold. On product of odd dimensionalspheres S2p+1 × S2q+1 with p > 0 or q > 0, complex structures were obtainedby H. Hopf (1948) and Calabi-Eckmann (1953). These complex manifolds areone of the first examples of non-K¨ahler, and hence non-projective, compactcomplex manifolds.The aim of this talk is to describe a general construction of a class ofnon-K¨ahler compact complex manifolds. Let G be a complex linear algebriacgroup and let K be a maximal compact subgroup of G. Any holomorphicprincipal G-bundle EG over a complex manifold admits a smooth reduction ofthe structure group from G to K. We will show that the total space EK of thesmooth principal K-bundle, corresponding to this reduction, admits a complexstructure. In most cases, the complex manifold EK will be non-K¨ahler. Thistalk is based on a joint work with Mainak Poddar.

Date/Time

Venue

Mathematics Department Seminar Hall

Speaker

Ritwik Mukherjee

Affiliation

NISER

Title

Integration on Manifolds

We will explain what it means to integrate differential forms on a manifold and state Stokes Theorem. We will see how it generalizes the fundamental theorem of calculus and Green's theorem.

Date/Time

Venue

SMS Seminar Hall

Speaker

Dr Saswata Adhikari

Affiliation

IIT Madras

Title

Frames of twisted shift-invariant spaces in $L^{2}(\mathbb{R}^{2n})$ and shift-invariant spaces on the Heisenberg group

**Abstract:** A well known result on translates of a function $\varphi$ in $L^{2}(\mathbb{R})$ states that the collection $\{\tau_{k}\varphi: k\in\mathbb {Z}\}$ forms an orthonormal system in $L^{2}(\mathbb{R})$ iff $p_{\varphi}(\xi)=\sum\limits_{k\in\mathbb {Z}}|\widehat{\varphi}(\xi+k)|^{2}= 1~ a.e.~ \xi\in\mathbb {T}$. Similarly in the literature there are interesting characterizations of Bessel sequence, frame, Riesz basis of a system of translates in $L^{2}(\mathbb{R})$ in terms of Fourier transform.In this talk, we aim to study frames in twisted shift-invariant spaces in $L^{2}(\mathbb{R}^{2n})$ and shift-invariant spaces on the Heisenberg group $\mathbb{H}^{n}$. First we shall define a twisted shift-invariant space $V^{t}(\varphi)$ in $L^{2}(\mathbb{R}^{2n})$ as the closed linear span of the twisted translates of $\varphi$. We shall obtain characterizations of orthonormal system, Bessel sequence, frame and Riesz basis consisting of twisted translates $\{T_{(k,l)}^{t}\varphi: k,l\in\mathbb{Z}^{n}\}$ of $\varphi\in L^{2}(\mathbb{R}^{2n})$ in terms of the kernel $K_{\varphi}$ of the Weyl transform of $\varphi$. In particular, we shall prove that if $\{T_{(k,l)}^{t}\varphi:k,l\in\mathbb{Z}^{n}\}$ is an orthonormal system in $L^{2}(\mathbb{R}^{2n})$, then $w_{\varphi}(\xi)=1$ a.e. $\xi\in\mathbb{T}^{n}$, where $w_{\varphi}(\xi)=\sum\limits_{m\in\mathbb{Z}^{n}}\int\limits_{\mathbb{R}^{n}}|K_{\varphi}(\xi+m,\eta)|^{2}d\eta,~\xi~\in\mathbb{T}^{n}$. Unlike the classical case on $\mathbb{R}^{n}$, it turns out to be a surprising fact that the converse of the above theorem need not be true. The converse is true with an additional condition, which we call "condition C". In fact, we shall see that $\{T_{(k,l)}^{t}\varphi:k,l\in\mathbb{Z}^{n}\}$ is an orthonormal system in $L^{2}(\mathbb{R}^{2n})$ if and only if $w_{\varphi}(\xi)=1$ a.e. $\xi\in\mathbb{T}^{n}$ and $\varphi$ satisfies condition C. Next we shall study shift-invariant spaces associated with countably many mutually orthogonal generators $\mathscr{A}$ on the Heisenberg group. We shall conclude the talk by providing a sampling formula on a subspace of a twisted shift-invariant space as an application of our results.

Date/Time

Venue

Conference Room, School of Mathematical Sciences

Speaker

Sabyasachi Mukhopadhyay

Affiliation

University of Hohenheim

Title

Modelling spatio-temporal variation in rainfall using a hierarchical Bayesian regression model

Date/Time

Venue

Mathematics Seminar Room

Speaker

Anindya Ghatak

Affiliation

SMS, NISER

Title

p-order ideals

TBA

Date/Time

Venue

Mathematics Seminar Room

Speaker

Anindya Ghatak

Affiliation

SMS, NISER

Title

Quantization of $A_0(K)$-spaces and $M$-ideals in matrix ordered spaces

Date/Time

Venue

SMS seminar room

Speaker

Biplab Paul

Affiliation

IIT G

Title

Some variations of EM algorithms for estimating parameters of singular Bivariate Marshall-Olkin Pareto distribution

Abstract : Here we study the Marshall-Olkin formulation of bivariate Pareto distribution, which includes both location and scale parameters and find efficient estimation techniques of the parameters of corresponding distribution. We use Maximum likelihood Estimation through the EM algorithm for the parameter estimation. Pareto distribution is heavy-tail in nature. It plays an important role in the Extreme Value Theory. So these distributions can be very useful in modeling the data related to finance, insurance, climate and network-security etc. These distributions can be used to analyze data related to any bivariate-component systems, e.g. axial length of two eyes of a diabetic patient. A numerical simulation is performed to verify the performance of different proposed algorithms

Date/Time

Venue

SMS seminar room

Speaker

Tanikella Padma Ragaleena

Affiliation

student of school of math sciences, NISER

Title

Theory of Regression Analysis with Applications

Regression analysis is a branch of statistics that provides us with tools to model a relationship between variables. In this presentation, we will discuss two types of regression models: the classical linear regression and non-parametric regression. Linear regression analysis aims to fit a linear model to data with the help of Least Square Estimates. For this model, we will discuss the techniques for checking the appropriateness of the model, the tests for determining the significance of regressor variables, the methods for dealing with multi-collinearity, and the procedure for incorporating categorical (or qualitative) variables into our regression model. We will also talk about a few topics from non-parametric regression such as density estimation and smoothing. Most of the concepts will be illustrated in statistical software R using real-life data-sets.

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Mr. A S Abdul Shabeer

Affiliation

SMS, NISER

Title

Hurwitz's Formula for Compact Riemann Surfaces

* Abstract:* Given a holomorphic map between compact Riemann surfaces, Hurwitz's formula relates the genera of the domain and range with the degree and ramification of the map. We will see a short proof of this and some of its applications. Necessary definitions will be recalled.

Date/Time

Venue

Online

Speaker

Mr. Arindam Mandal

Affiliation

SMS, NISER

Title

Gelfand - Naimark - Segal Construction.

**Abstract:** I shall talk about the Gelfand-Naimark-Segal construction and prove that any general C*-algebra is isometrically ∗-isomorphic to a norm closed subalgebra of B(H) for some Hilbert space H.

Date/Time

Venue

LH 101

Speaker

Professor A. Sankaranarayanan

Affiliation

TIFR, Mumbai

Title

Riemann zeta-function and it's influence on a problem of Srinivasa Ramanujan

Abstract : We discuss about the large values of the Riemann zeta-function on the line $1$ and it's consequence to the error term of the summatory function of $d^2(n)$ for $1 \le n \le x$ for large $x$ considered by Srinivasa Ramanujan where $d(n)$ denotes the sum of the positive divisors of the positive integer $n$.

Date/Time

Venue

M 4

Speaker

Dinesh Kumar Keshari

Affiliation

Indian Institute of Science Bangalore

Title

Curvature inequalities for operators in the Cowen–Douglas class

The curvature of a contraction T in the Cowen-Douglasclass is bounded above by the curvature of the backward shiftoperator. However, in general, an operator satisfying thecurvature inequality need not be contractive. In this talk wecharacterize a slightly smaller class of contractions using astronger form of the curvature inequality. Along the way, we findconditions on the metric of the holomorphic Hermitian vectorbundle E corresponding to the operator T in the Cowen-Douglasclass which ensures negative definiteness of the curvaturefunction. We obtain a generalization for commuting tuples ofoperators in the Cowen-Douglas class.

Date/Time

Venue

Mathematics Seminar Room

Speaker

TSSRK Rao

Affiliation

ISI, Bangalore

Title

Almost isometric ideals in Banach spaces

In this talk we introduced the notion of an almost isometric ideal based on the Principle of Local reflexivity and study its properties.

The talk will also be accessible to students who had a first course in Functional Analysis.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Dr. Samik Basu

Affiliation

Ramakrishna Mission Vivekananda University

Title

Homotopy groups of highly connected manifolds

We shall discuss a new method of computing (integral) homotopy groups of certain manifolds in terms of the homotopy groups of spheres. The techniques used in this computation also yield formulae for homotopy groups of connected sums of sphere products and CW complexes of a similar type. In all the families of spaces considered here, we verify a conjecture of J. C. Moore. This is joint work with Somnath Basu.

Date/Time

Venue

Mathematics Seminar Room

Speaker

Anil Kumar Karn

Affiliation

NISER, SMS

Title

A model for non-commutative vector lattices

We shall begin with a characterization of algebraic orthogonality in C^*-algebras in terms of order and norm. We apply this chacterization to propose a model of ``Absolutely ordered spaces'' which turns out to be a vector lattice under `commutative' conditions. This model suits to operator algebras and has potential to be applicable in quantum theory.

Date/Time

Venue

SMS Seminal Hall

Speaker

Mr. Sayan Ghosh

Affiliation

IIT Bombay

Title

The Analysis of Incomplete Contingency Tables

Abstract: The analysis of incomplete contingency tables is an interesting problem, which is also of practical interest. In this talk, we propose various missing data models for analyzing arbitrary three-way and multidimensional incomplete tables, and study estimation and testing under them. We also explore the problem of boundary solutions in such tables, proposing their various forms, connections among them and establishing sufficient and necessary conditions for their occurrence (using only the observed cell counts), which prove useful for model selection. Finally, we suggest methods for assessment of the missing data mechanisms of variables in the above tables in terms of only the observed cell counts.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Karen Strung

Affiliation

Radboud University - Radboud University

Title

C*-algebras, Dynamical Systems, and Classification

Simple unital nuclear C*-algebras, assuming a minor finiteness condition and the so-called UCT, can be classified up to *-homomorphisms by an invariant consisting of K-theory, traces, and a pairing between these objects. I will discuss the classification of such C*-algebras by focussing on the classification for C*-algebras arising from two interesting classes of dynamical systems: minimal homeomorphisms with mean dimension zero and mixing Smale spaces.In my fist lecture I will introduce the classification programme as well as the construction of C*-algebra from dynamical systems via crossed products and groupoids.In my second lecture, I will discuss properties and detail the classification of the two classes mentioned above.

Date/Time

Venue

LH-5

Speaker

Parameswaran Shankaran

Affiliation

IMSc Chennai

Title

The geometry of the upper half-space

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Anish Ghosh

Affiliation

TIFR Mumbai

Title

An introduction to equidistribution

I will discuss the distribution of some arithmetic and geometric objects and describe the basic tools used to study questions of equidistribution.

Date/Time

Venue

Mathematics Seminar Room

Speaker

Amit Kumar

Affiliation

NISER

Title

Partial isometries in absolute matrix order unit spaces

In this talk, we shall introduce the notions of absolutely matrix ordered spaces and absolute matrix order unit spaces in the context of matrix ordered spaces. We shall prove that a unital, bijective $\ast$-linear map between absolute matrix order unit spaces is a complete isometry if, and only if, it is a completely absolute value preserving. From here, we deduce that on (unital) C$^*$-algebras such maps are precisely C$^*$-algebra isomorphisms. We shall extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We shall introduce the notion of a partial isometry in an absolute matrix order unit space to describe the comparison of order projections. We shall also discuss direct limit of absolute matrix order unit spaces to show the existence of ``Grothendieck group" through order projections and prove that ``Grothendieck group" is a functor from category of ``absolute matrix order unit spaces with morphisms as unital completely absolute preserving maps" to category of ``abelian groups". Later, we define orthogonality of complete absolute preserving maps and prove that ``Grothendieck group" functor is additive on orthogonal unital completely absolute preserving maps.

Date/Time

Venue

Online

Speaker

Devashish Sonowal

Affiliation

SMS, NISER

Title

Taylor's theorem from the viewpoint of heat equation

Abstract: Employing solution of heat equation, we prove Taylor's theorem with Peano form of the remainder. In addition, we derive the Taylor series of an infinitely differentiable function under the additional assumption that the n'th derivative does not grow faster than the n'th power of some fixed positive constant.

**Googlemeets link**: https://meet.google.com/pdg-ymra-wkv

All are cordially invited.

Date/Time

Venue

Online

Speaker

Ms. Anuvertika Pandey

Affiliation

SMS, NISER

Title

The Whitney Embedding Theorem.

**Abstract:** In this talk, we will prove a fundamental theorem on differential geometry, namely the embedding theorem due to Hassler Whitney, which shows that every smooth manifold can be embedded into a Euclidean space.

Date/Time

Venue

LH-101

Speaker

Subham Giridhar

Affiliation

SMS, NISER

Title

Elementary Number Theory

**Abstract**: In this talk, using the basics of the Arithmetic that was learned in school, some of the elementary theorems of Number theory will be proven and also a flavor of RSA encryption will be given using the theory discussed.

The prerequisite to attend this talk is just to have a basic high school (till 10th) background in Mathematics.

All are cordially invited

Date/Time

Venue

PL-8

Speaker

Dr. B G Manjunath

Affiliation

Bussiness Analysis Adviser, Dell International Services Pvt. Ltd.

Title

Gaussian structure of non-Gaussian distributions and contemporary theorems

Classical distribution theory in higher dimensions is largely focused on the Gaussian distribution. However, for the Gaussian distribution it is well known that every marginal distribution, every conditional distribution and all linear transformations are also Gaussian. Besides, it is also obvious that these properties chosen individually are not sufficient conditions to characterize the Gaussian distribution. There are many non-Gaussian distributions which share some of these features with the Gaussian distribution. In the present talk we introduce couple of new theorems which characterizes the Gaussian distribution. Besides, one of the extensive application of the Gaussian distribution will be in classical classification theory. In the current note we also discusses the extensions of classical classification results to the theory of extreme value analysis. Problem in action: Let P and Q be a two sets of probability measures defined on the same sigma field. Let T be a transformation which maps every measure from P to one and only measure in Q. Now, given Q and T can we characterize the set P ?

Date/Time

Venue

M3

Speaker

Sutanu Roy

Affiliation

Carleton University, Canada

Title

Faithful actions of locally compact quantum groups on classical spaces

A rigidity conjecture by Goswami states that existence of a smooth and faithful action of a compact quantum group G on a compact connected Riemannian manifold M forces G to be compact group. In particular, whenever the action is isometric, or G is finite dimensional, Goswami and Joardar have proved that the conjecture is true. The first step in the investigation of a non-compact version of this rigidity conjecture demands a correct notion of faithful actions of locally compact quantum groups on classical spaces. In this talk, we show that bicrossed product construction for locally compact groups provides a large class of examples of non-Kac locally compact quantum groups acting faithfully and ergodically on classical (non-compact) spaces. However, none of these actions can be isometric, leading to the aforementioned rigidity conjecture may hold in the non-compact case as well. This is based on the joint work in progress with Debashish Goswami.

A rigidity conjecture by Goswami states that existence of a smooth and faithful action of a compact quantum group G on a compact connected Riemannian manifold M forces G to be compact group. In particular, whenever the action is isometric, or G is finite dimensional, Goswami and Joardar have proved that the conjecture is true. The first step in the investigation of a non-compact version of this rigidity conjecture demands a correct notion of faithful actions of locally compact quantum groups on classical spaces. In this talk, we show that bicrossed product construction for locally compact groups provides a large class of examples of non-Kac locally compact quantum groups acting faithfully and ergodically on classical (non-compact) spaces. However, none of these actions can be isometric, leading to the aforementioned rigidity conjecture may hold in the non-compact case as well. This is based on the joint work in progress with Debashish Goswami. - See more at: http://sms.niser.ac.in/news/seminar-57#sthash.QhHWSEq6.dpuf

A rigidity conjecture by Goswami states that existence of a smooth and faithful action of a compact quantum group G on a compact connected Riemannian manifold M forces G to be compact group. In particular, whenever the action is isometric, or G is finite dimensional, Goswami and Joardar have proved that the conjecture is true. The first step in the investigation of a non-compact version of this rigidity conjecture demands a correct notion of faithful actions of locally compact quantum groups on classical spaces. In this talk, we show that bicrossed product construction for locally compact groups provides a large class of examples of non-Kac locally compact quantum groups acting faithfully and ergodically on classical (non-compact) spaces. However, none of these actions can be isometric, leading to the aforementioned rigidity conjecture may hold in the non-compact case as well. This is based on the joint work in progress with Debashish Goswami. - See more at: http://sms.niser.ac.in/news/seminar-57#sthash.QhHWSEq6.dpuf

A rigidity conjecture by Goswami states that existence of a smooth and faithful action of a compact quantum group G on a compact connected Riemannian manifold M forces G to be compact group. In particular, whenever the action is isometric, or G is finite dimensional, Goswami and Joardar have proved that the conjecture is true. The first step in the investigation of a non-compact version of this rigidity conjecture demands a correct notion of faithful actions of locally compact quantum groups on classical spaces. In this talk, we show that bicrossed product construction for locally compact groups provides a large class of examples of non-Kac locally compact quantum groups acting faithfully and ergodically on classical (non-compact) spaces. However, none of these actions can be isometric, leading to the aforementioned rigidity conjecture may hold in the non-compact case as well. This is based on the joint work in progress with Debashish Goswami. - See more at: http://sms.niser.ac.in/news/seminar-57#sthash.QhHWSEq6.dpuf

Date/Time

Venue

Seminar Room, SMS

Speaker

Dr. Anirban Mukhopadhyay

Affiliation

IMSc. Chennai

Title

Distribution of Primes

In this lectures, we would discuss probabilistic model of primes leading to heuristics about their distribution. We would see many surprising irregularities popping up alongside expected results. A survey of several recent and important results would be presented in a way accessible to non-experts.

Date/Time

Venue

Mathematics Seminar Hall

Speaker

Ritwik Mukheree

Affiliation

NISER

Title

Introduction to Geometric Analysis

We will define what is a Laplacian on a smooth Riemannian Manifold. We will then define what are harmonic forms and state the Hodge Decomposition Theorem. In particular, we will explain how it implies Poincare Duality. We will then go on to define the notion of a weak solution and explain how elliptic regularity of the Laplacian, implies the Hodge Decomposition Theorem. We will review the basic notions of smooth manifolds and keep prerequisites to a minimum. Those who are interested in Analysis and PDE are encouraged to attend.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Ami Viselter

Affiliation

University of Haifa, Israel

Title

Locally compact quantum groups: the von Neumann algebraic approach-2

Lecture series abstract: We will survey the von Neumann algebraic approach to locally compact quantum groups in the sense of Kustermans and Vaes, roughly following the treatment by Van Daele. We will begin with an intro to the theory of weights of von Neumann algebras. We will then proceed to describe locally compact quantum groups. If there is any time left, we will present some recent progress in the field. The prerequisite for attending the talks is some basic knowledge of C*-algebras (and perhaps also von Neumann algebras, depending on the audience).

Date/Time

Venue

Seminar Room, SMS

Speaker

Professor Komatsu Takao

Affiliation

Wuhan University

Title

Several identities related to the degenerate Bernoulli polynomials and numbers

In this talk we demonstrate some relations in degenerate Bernoulli polynomials , which may be expressed as a general convolution identity. We also show some properties of hypergeometric degenerate Bernoulli polynomials and numbers.

Date/Time

Venue

SMS Conference Room

Speaker

Abhrojyoti Sen

Affiliation

NISER Bhubaneswar

Title

LIMITING BEHAVIOR OF SOLUTIONS FOR SOME STRICTLY HYPERBOLIC SYSTEMS OF CONSERVATION LAWS

We study the limiting behavior of the solutions of Euler equations of one-dimensional compressible fluid flow as the pressure like term vanishes. This system can be thought of as an approximation for the one dimensional model for large scale structure formation of universe. We show that the solutions of former equation converges to the solution of later in the sense of distribution and agrees with the vanishing viscosity limit when the initial data is of Riemann type.

Date/Time

Venue

SMS Seminar Room

Speaker

Moni Kumari

Affiliation

TIFR, Mumbai

Title

TBA

TBA

Date/Time

Venue

Mathematics Conference Room

Speaker

Amit kumar

Affiliation

NISER

Title

Isometries of absolute order unit spaces

Date/Time

Venue

SMS seminar hall

Speaker

Archana S

Affiliation

NISER

Title

Heke Bochner Formula for Euclidean Fourier transform

Date/Time

Venue

Online (Google Meet)

Speaker

Tanikella Padma Ragaleena

Affiliation

NISER, SMS

Title

Selected classification techniques

**Abstract:**

Statistical classification techniques attempt to predict the true class label of a new observation (i.e. an observation not used in the construction of the classifier) based on a set of observations whose class labels are known beforehand. During the presentation, we will discuss the following classification methods - linear discriminant analysis, quadratic discriminant analysis, Fisher discriminant analysis, decision tree classifier, and artificial neural network classifier. Underlying assumptions of each of these techniques along with how each of these methods work will be discussed.

**Google Meet Link: ****https://meet.google.com/gce-weco-wai**

Date/Time

Venue

Online

Speaker

Ms. Anuvertika Pandey

Affiliation

SMS, NISER

Title

Toeplitz Operators on the Hardy Space.

**Abstract:** We will characterize Toeplitz operators on the Hardy space using Berezin transform and then we will derive the necessary and sufficient condition under which two Toeplitz operators commute.

Date/Time

Venue

LH-101

Speaker

Dr. Mahabir Prasad Jhanwar

Affiliation

University of Calgary, Canada

Title

Cryptographic Accumulators using Lattices

We provide the first accumulator scheme based on lattices. The security of our scheme is based on the "small integer solution (SIS)" problem, which is known to be as hard as approximating certain worst-case problems on lattices to within small approximating factors. Our lattice-based construction offers the hope of withstanding quantum computers, against which both discrete-log and factoring-based approaches are known to be utterly defenseless.

Date/Time

Venue

LH 101

Speaker

Dr. Vishnu Narayan Mishra

Affiliation

Sardar Vallabhbhai National Institute of Technology

Title

Approximation of functions by positive linear operators

Positive approximation processes play an important role in Approximation Theory and appear in a very natural way dealing with approximation of continuous functions, especially one, which requires further qualitative properties such as monotonicity, convexity and shape preservation and so on. In this talk, we discuss the degree of approximation of signals (functions) using various types of summability transforms methods in different spaces. Approximation of functions by positive linear operators using Quantum calculus (q-calculus) will also be highlighted. During this talk, few applications of approximations of functions will also be highlighted.

Date/Time

Venue

M1

Speaker

Professor Probal Chaudhuri

Affiliation

Indian Statistical Institute, Kolkata

Title

Shape of the Earth, Motion of the Planets and the Method of Least Squares

Abstract In the 18th century, while dealing with astronomical and geodesic measurements, the scientists were confronted with a statistical problem, which in those days was described as "the problem of combining inconsistent equations". People who worked on this problem and contributed towards its solutions include Euler, Laplace, Gauss and Legendre among many others. I shall discuss the history of the problem and how it eventually led to the invention of the method of least squares.

Date/Time

Venue

SMS seminar room

Speaker

Bikramaditya Sahu

Affiliation

NISER-Bhubaneswar

Title

Blocking sets of PG(2,q) with respect to a conic

For a given nonempty subset L of the line set of the projective plane PG(2,q), a blocking set with respect to L (or simply, an L-blocking set) is a subset B of the point set of PG(2,q) such that every line of L contains at least one point of B. Let E (respectively; T, S) denote the set of all lines which are external (respectively; tangent, secant) to an irreducible conic in PG(2,q). We shall discuss minimum size L-blocking sets of PG(2,q) for L = E, S, T, SUT, EUT, SUE.

Date/Time

Venue

Mathematics Seminar Hall

Speaker

Somnath Basu

Affiliation

IISER Kolkata

Title

Geometric models of coverings of graphs

We shall discuss covering spaces of graphs, leading to facts about subgroups of free groups.We shall then construct geometric models, inspired by these graphs,and analyze some concrete examples.

Date/Time

Venue

SMS Seminar Room

Speaker

Antar Bandyopadhyay

Affiliation

Indian Statistical Institute, New Delhi

Title

Random Graphs (2nd Lecture)

**This is a Short Lecture Series in Mathematics (SLSM) consisting of 4 lectures of 90 minutes each. This is the second lecture in this series.**

**Abstract:** The first half of the mini course will be an introducing to the two classical models of random graphs (a.k.a. Erdős-Rényi random graphs) and discuss the phenomenon of phase transition. We will also discuss thresholds for monotonic properties with examples including connectivity threshold and sub-graph containment threshold.

In the second half of the course we will consider other kind of random graphs. In particular, we will discuss various models for complex networks, including Albert-Barabási preferential attachment models. We will discuss "scale-freeness", asymptotic degree distribution and "small-world phenomenon". Properties of super and sub-linear preferential attachment models and some recent developments in de-preferential attachment models will also be discussed.

If time permits we will also introduce the random geometric graphs and discuss asymptotic of the connectivity threshold.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Swagato K Ray

Affiliation

ISI Kolkata

Title

On limits of ball averages

In 1931 Plancherel and Polya observed the following amusing fact: If the averages of a locally integrable function on \mathbb R over balls of radius R with center x converges to f(x) for all x as R goes to infinity then f(x)=ax+b for some real numbers a and b. They went on to show that in higher dimension the limit of ball averages is a harmonic function. We shall talk about a generalization of this result for Riemannian symmetric spaces of noncompact type with rank one.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Aprameyan Parthasarathy

Affiliation

Universität Paderborn

Title

TBA

TBA

Date/Time

Venue

M1

Speaker

Santu Pal

Affiliation

JRF

Title

A Conditional Differential Cryptanalysis on the Stream Cipher Grain-v1

The talk contains a type of differential cryptnalysis on a popular stream cipher (Grain v1) with some conditions on IV bits.

Date/Time

Venue

M1

Speaker

Madhav Reddy Bagannagari

Affiliation

ISI Kolkata

Title

Free-type rigid C*-tensor categories and their annular representations

C*-tensor categories are important descriptors of generalized symmetries appearing in non-commutative analysis and mathematical physics. An important algebra associated to a rigid semisimple C*-tensor category $ \mathcal{C} $ is the tube algebra $ \mathcal{A}\mathcal{C} $. The tube algebra admits a universal C*-algebra, hence has a well behaved representation category. Further, this representation category provides a useful way to describe the analytic properties of initial C*-tensor categories, such as amenability, the Haagerup property, and property (T).With a brief motivation from different directions, in this talk, I will move on to describing the annular algebra $\mathcal{A}\Lambda$ associated to a rigid C*-tensor category $ \mathcal{C} $. The annular representation category of $ \mathcal{C} $ is the category of $*$-representations of the annular algebra $\mathcal{A}\Lambda$. I will then present a description of the annular representation category of free product of two categories with an application to the Fuss-Catalan subfactor planar algebra.We then move onto oriented extensions of subfactor planar algebras (or equivalently singly generated C*-2-categories), which are a class of singly generated C*-tensor categories (or equivalently oriented factor planar algebras). I will end the talk with few problems which could extend this work.

Date/Time

Venue

SMS seminar room

Speaker

Soumendu Sundar Mukherjee

Affiliation

Indian Statistical Institute Kolkata

Title

On offline changepoint estimation for network data

We consider the problem of offline changepoint estimation in a network-valued time series where the entire series is observed beforehand. We analyze a CUSUM statistic for this problem, and obtain, under minimal conditions, the rate of convergence of the resulting changepoint estimator in terms of three relevant parameters: (i) the (common) network size, (ii) the (common) network sparsity, and (iii) the total number of networks in the series. We also discuss some applications. This is based on on- going joint work with Peter Bickel, Sharmodeep Bhattacharyya, and Shirshendu Chatterjee.

Date/Time

Venue

Conference Room, School of Mathematical Sciences

Speaker

Rekha Biswal

Affiliation

Max Planck Institute for Mathematics, Bonn

Title

Macdonald polynomials and level two Demazure modules for affine sl_{n+1}

Date/Time

Venue

Online (Google Meet)

Speaker

Samriddho Roy

Affiliation

TIFR-Centre for Applicable Mathematics

Title

Complex Geometry of a family of domains related to $\mu$-synthesis and the Lempert Theorem

Abstract:- See the attached file.

**Google Meet Link: **meet.google.com/zxe-csox-oyb

Date/Time

Venue

Online (GoogleMeet)

Speaker

Swadeepta Mandal

Affiliation

NISER Bhubaneswar

Title

Quantum zero - error communication

We will talk about the basic concept of quantum zero-error, zero-error capacity of a quantum channel and some of its properties. Then we will look at superactivation phenomenon which is exclusive to quantum setup and the quantum version of Lov´asz function.

Date/Time

Venue

PL8

Speaker

Dr. Rahul Garg

Affiliation

Israel Institute of Technology, Haifa, Israel

Title

The lattice point counting problem on the Heisenberg groups

**Abstract : **I shall begin with the description of the lattice points counting problem in Euclidean spaces. Namely, establishing an (asymptotic) error estimate for the number of points that the lattice of integral points has in a Euclidean ball of large radius, as the radius goes to infinity.

This problem has a very long history and vast literature is available in obtaining error estimates for Euclidean dilates of the unit ball as well as various other convex bodies.

In the first half of the talk, I shall sketch the Fourier spectral method which originated with Minkowski for Euclidean balls. This classical method does not give the best possible error estimates for the balls, but it gives optimal error in the class of Euclidean dilates of convex bodies with surfaces having non-vanishing Gaussian curvature at all points.

In the last half of the talk, I shall discuss the lattice points counting problem in the context of the Heisenberg groups, for families of balls corresponding to certain radial and homogeneous norms, including the canonical Cygan-Koranyi norm.

None of the Euclidean results apply to this problem simply because of the non-isotropic character of the Heisenberg dilation. We note that in some cases our error estimates are the best possible in all dimensions.

In the end, I shall briefly mention the scope of this method discussing more general nilpotent Lie groups.

This talk is based on my joint work with Amos Nevo and Krystal Taylor which is available on arXiv. Most of this talk should be accessible to those who are familiar with basic functional analysis.

Date/Time

Venue

LH-105

Speaker

Dr. Shirshendu Chowdhury

Affiliation

TIFR-CAM, Bangalore

Title

Controllability of Linearized Compressible Navier Stokes equations

Abstract: We will describe: (i) What is Controllability problem (ii) Examples and known results: ODE (finite dim), transport equation, Heat equation (infinite dim ). Then we consider compressible Navier-Stokes equations in one dimension, linearized around a constant steady state $(Q_0,V_0)$, with $Q_0 > 0,V_0\geq 0$. It is a coupled system involving both transport and parabolic effects. We study the controllability of this linearized system in bounded interval $(0,L)$. We find that the properties of the two semigroups $(e^{tA})_{t\geq0} $ (the one when $V_0 = 0$ and the one when $V_0> 0$) and the spectrum of $A$ are completely different where $A$ is the corresponding linearized operator. We obtain several interesting positive and negative results for the null controllability and approximate controllability of the system using interior or boundary control in both the cases $V_0 =0$ and $V_0>0$.

Date/Time

Venue

LH-5

Speaker

Prof. K.T. Joseph

Affiliation

TIFR CAM

Title

ON HYPERBOLIC SYSTEMS OF CONSERVATION LAWS

Hyperbolic systems of conservation laws appear in many different areain Physics and has a history of more than 200 years. It became part of the morderntheory of analysis of PDES just 65 years ago. Now this theory is a well developedbranch of Analysis. Aim of this talk is to tell this story. The first part of thetalk is concerned with the Lax- Glimm theory of classical shocks and wellposednessof initial value problem. The second part is on initial boundary value problemfor systems and different formulation based on entropy inequalities and boundarylayers. We touch up on the recent work in the subject with Anupam Pal Chaudhuryand P.G.LeFloch

Date/Time

Venue

Mathematics Seminar Hall

Speaker

Gopinath Panda

Affiliation

IIT, Bhubaneswar

Title

Optimal Balking Strategies in Markovian Queues with Vacations

Abstract: Queueing theory is vastly used to study service systems arising in management problems, where customers are considered to be indifferent in the sense that the decisions to control a system, are only made by the management and the users are impelled to follow the decisions. However, for a service system to be more realistic, it is essential to consider customers’ decisions about their actions (join or balk, wait or abandon, buy priority or not) which depends on the information provided to them at their arrival epochs. The study of queuing systems with strategic customers was initiated by Naor in 1969. After Naor’s work, an emerging tendency to study customers’ behavior imposing a reward-cost structure on the system took place. In this scenario, customers want to maximize their net benefit against others who have the same objective, which can be viewed as a symmetric game among them. When the system is empty, the server goes on vacation and returns after a random time to serve waiting customers if any.During the server’s vacation, customers continue to arrive at the system and if the present customers did not receive their service in due time, they became impatient and decide sequentially whether they will abandon the system or not upon the availability of a secondary transportation facility. In this presentation, the focus is to study customers’ equilibrium and socially optimal behavior in queuing systems with server vacation. Numerical experiments showing the dependence of performance measures on system parameters is demonstrated via several figures. Finally, a potential application of the model is suggested in managing a perishable inventory store.

Date/Time

Venue

SMS Seminar Hall

Speaker

Prof. Bart De Bruyn

Affiliation

Ghent University, Belgium

Title

Finite Fields

This will be the fourth lecture of a series of five on Finite Fields.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Partha Sarathi Chakraborty

Affiliation

IMSc

Title

Instances of local index formula

Local Index formula is at the heart of the so called hard Riemannian aspects of Noncommutative Geometry. We will try to see why thisis so important. However so far we have only one computation of the local index formula. We will discuss two more computations.

Date/Time

Venue

SMS Seminar Hall

Speaker

Mr. Mithun Bhowmick

Affiliation

ISI Kolkata

Title

Theorems of Ingham, Levinson and Paley-Wiener on certain Lie groups

Abstract: In this talk, our focus will be on certain classical results due to Ingham, Levinson and Paley-Wiener which find optimal decay of the Fourier transform of nonzero functions vanishing on `large sets'. We will talk about these theorems in details and their generalizations on the $n$- dimensional Euclidean space, the $n$-dimensional torus and certain non-commutative Lie groups.

Date/Time

Venue

Conference Room, School of Mathematical Sciences

Speaker

Atibur Rahaman

Affiliation

NISER Bhubaneswar

Title

Braided quantum E(2) groups

Date/Time

Venue

SMS Seminar Room

Speaker

Dr. Soumya Bhattacharya

Affiliation

IISER, Kolkata

Title

Finiteness results on a certain class of modular forms and applications

Holomorphic eta quotients' are certain explicit classicalmodular forms on suitable Hecke subgroups of the full modular group.We call a holomorphic eta quotient $f$ 'reducible' if for someholomorphic eta quotient $g$ (other than 1 and $f$), the eta quotient$f/g$ is holomorphic. An eta quotient or a modular form in generalhas two parameters: Weight and level. We shall show that for anypositive integer $N$, there are only finitely many irreducible holomorphiceta quotients of level $N$. In particular, the weights of such eta quotientsare bounded above by a function of $N$. We shall provide such an explicitupper bound. This is an analog of a conjecture of Zagier which says thatfor any positive integer $k$, there are only finitely many irreducibleholomorphic eta quotients of weight $k/2$ which are not integral rescalingsof some other eta quotients. This conjecture was established in 1991 byMersmann. We shall sketch a short proof of Mersmann's theorem and weshall show that these results have their applications in factorizingholomorphic eta quotient. In particular, due to Zagier and Mersmann's work,holomorphic eta quotients of weight $1/2$ have been completely classified.We shall see some applications of this classification and we shall discussa few seemingly accessible yet longstanding open problems about etaquotients. This talk will be suitable also for non-experts: We shall define all therelevant terms and we shall clearly state the classical results which we use.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Sk Asfaq Hossain

Affiliation

ISI Kolkata

Title

Quantum Symmetry on Potts Model

Potts Model is a model of interacting spins on a crystalline lattice. In this talk we try to define the notion of Quantum Symmetry for Potts Model and try to explore the relations between Quantum Symmetry on Potts Model and Quantum Symmetry of the underlying graph structure. This is based On Joint work with Prof. Debashish Goswami.

Date/Time

Venue

SMS Conference Room

Speaker

Rohit Kumar Mishra

Affiliation

University of Texas at Arlington

Title

Uniqueness and Injectivity questions for certain integral transforms

Date/Time

Venue

Online (GoogleMeet)

Speaker

Keshab Chandra Bakshi

Affiliation

CMI

Title

Pimsner-Popa basis and angle between intermediate subalgebras

Date/Time

Venue

Online

Speaker

Mr. Nilkantha Das.

Affiliation

SMS, NISER

Title

Enumerative geometry of curves in a moving family of surfaces.

**Abstract**: Enumerative geometry of curves in the complex projective plane is very classical. In this talk, we consider two generalisations of classical enumerative geometric problems of curves in the plane. We consider curves in that lie inside a in ; such curves are called *planar* curves. We discuss the enumeration of degree planar curves in having nodes and another singularity of codimension , and that intersect generic lines and pass through generic points in , where with . We also count the number of elliptic () curves of degree in a del Pezzo surface that pass through generic points of .

Date/Time

Venue

LH-101

Speaker

Moni Kumari

Affiliation

NISER, Bhubaneswar

Title

Euler's famous prime generating polynomial

Date/Time

Venue

PL-8

Speaker

Dr. Amit Chattopadhyay

Affiliation

School of Computing, University of Leeds, U.K.

Title

Topological Data Analysis and Certified Geometry

Abstract: In this talk, first I will give a brief overview of my current research activities on topological data analysis, certified geometry, optimization and level set method with applications in visualization, graphics, image analysis and simulations.Then, I will present a recent work on multivariate (or multifield) topology simplification. Topological simplification of scalar and vector fields is well-established as an effective method for analyzing and visualizing complex data sets. For multifield data, topological analysis requires simultaneous advances both mathematically and computationally. Mathematically, weshow that the projection of the Jacobi Set of multivariate data into the Reeb Space produces a Jacobi Structure that separates the Reeb Space into components. We also show that the dual graph of these components gives rise to a Reeb Skeleton that has properties similar to the scalar contour tree and Reeb Graph, for topologically simple domains. Computationally, we show how to compute Jacobi Structure, Reeb Skeleton in an approximation of the Reeb Space, and that these can be used for visualization in a fashion similar to the contour tree and Reeb Graph.

Date/Time

Venue

Seminar Room, SMS

Speaker

Dr. Prem Prakash Pandey

Affiliation

HRI, Allahabad

Title

Square free values of polynomials

It is conjectured that all separable polynomials with integers coefficients, under some local conditions, take infinitely many (in fact positive density of) square free values on integer arguments. But not a single polynomial of degree greater than $3$ is proven to exhibit this property. We report on some progress towards showing that ``cyclotomic polynomial$\Phi_{\ell}(X)$ take square free values with positive proportion".

Date/Time

Venue

Seminar Room, Mathematics Department

Speaker

Ritwik Mukherjee

Affiliation

NISER

Title

Introduction to Smooth Manifolds

We will continue with the discussion on (co)tangent space and smooth maps. We will define what is the differential of a smooth map and state the implicit function theorem. We will also work out some concrete examples.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Dr. Anirban Bose

Title

Real elements in groups of type F4

Date/Time

Venue

Math Conference Room

Speaker

Sudeep Stephen

Affiliation

The University of Newcastle, Australia

Title

Zero forcing in graphs

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Kaushik Majumder

Affiliation

ISI Kolkata

Title

Problems and Results in uniform intersecting families.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Jaydeb Sarkar

Affiliation

ISI Bangalore

Title

Isometries on Hilbert spaces

We will describe the structure of isometries on Hilbert spaces, following H. Wold and J. von Neumann. Then we will proceed to represent (concrete and not so concrete) tuples of commuting isometries. We will draw a list of observations on subtlety of this object and link it up with some deep problems in operator theory and function theory. We will also report on some recent results concerning invariant subspaces of the Hardy space over the unit polydisc.

Date/Time

Venue

LH 5

Speaker

Professor Probal Chaudhury

Affiliation

ISI Kolkata

Title

Optimization by Monte Carlo

Abstract : I shall discuss how Monte Carlo methods can be used to solve complex optimization problems. In particular, I shall discuss the simulated annealing algorithm.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Santosh Nadimpalli

Affiliation

Radboud University, Nijmegen

Title

Whittaker models for cuspidal representations of p-adic unitary groups

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Ashish Mishra

Affiliation

Universidade Federal Do Pará

Title

On representation theory of partition algebras for complex reflection groups

A basis of the centralizer algebra for the action of the complex reflection group G(r, p, n) on the tensor product of its reflection representa- tion was given by Tanabe, and for p = 1, the corresponding partition algebra was studied by Orellana. In this talk, we first define the partition algebra for G(r, p, n) and call it Tanabe algebra. Along with the corresponding Schur–Weyl duality, using a confluence of ideas from Okounkov–Vershik approach, Clifford theory and higher Specht polynomials, we give a parametrization of the irreducible modules of Tanabe algebras and construct the Bratteli dia- gram. Furthermore, we give Jucys–Murphy elements and their actions on the canonical Gelfand–Tsetlin basis of irreducible modules of Tanabe algebras. In the process, we also obtain some new results in the representation theory of complex reflection groups. The results presented in this talk form a part of a joint work with Dr. Shraddha Srivastava.

Date/Time

Venue

Online (GoogleMeet)

Speaker

Sumana Hatui

Affiliation

IISc Bangalore

Title

On Schur multiplier and projective representations of groups

The study of projective representations has a long history starting with the pioneering work of Schur for finite groups (1904). It involves understanding the homomorphisms from a group into the projective general linear groups. Two essential ingredients to study the group’s projective representations are describing its Schur multiplier and representation group. In the first half of my talk, l shall start with a brief introduction to this topic. Then we shall discuss about the Schur multiplier of p-groups and give a characterization of non-abelian p-groups having Schur multiplier of maximum order. In the second half, we shall study the projective representations of discrete Heisenberg groups by describing its Schur multiplier and representation group. I shall finish my talk by discussing some future problems in this direction.

Date/Time

Venue

LH-101

Speaker

Dr. Kailash C. Misra

Affiliation

North Carolina State University, Raleigh, North Carolina, USA

Title

Lie algebras and Combinatorial Identities

Abstract:

The Lie groups were discovered by Sophus Lie around 1880 while searching for a framework to analyze the continuous symmetries of differential equations in much the same way as permutation groups are used in Galois theory for analylyzing the discrete symmetries of algebraic equations. One of the important idea in the theory of Lie groups is to replace the gobal object, the group, with its local or linearized version which Lie called its “infinitesimal group”, now known as its Lie algebra. Around 1940, after Elie Cartan’s beautiful classification of finite dimensional semisimple Lie algebras, Lie algebras emerged as an independent branch of Algebra. An important class of infinite dimensional Lie algebras generalizing the finite dimensional semisimple Lie algebras were discovered independently by Victor Kac and Robert Moody in 1968. An important family of these infinite Lie algebras is known as affine Lie algebras. These Lie algebras have proved to be very important with interactions in many areas of mathematics and physics. One such interaction is with number theory, particularly combinatorial identities. In this talk I will give an overview of some applications in this direction.

Date/Time

Venue

LH 2

Speaker

Dr. Rajesh Kumar

Affiliation

IIT Bhubaneswar

This talk consists of two parts. In the first part, we discuss the convergence of finite volume method for solving non-linear aggregation-breakage equation. The pro of re lie s on showing the consistency of the scheme and Lipschitz continuity of numerical fluxes. It is investigated that the technique is second order convergent independently of the meshes for pure breakage problem while for aggregation and coupled problems, it depends on the type of grids chose n for the computations. Next, we show the efficient representation of d-point correlation functions for a Gaussian random field. To avoid the curse of dimensionality for d > 2, a truncated KarhunenLo´eve expansion of the random field is used together with the low rank Tensor Train decomposition. The target application of this work is the computation of statistics ofthe solution of linear PDEs with random Gaussian forcing terms.

Date/Time

Venue

SMS seminar hall

Speaker

Atreyee Bhattacharya

Affiliation

RamaKrishna Mission Vivekananda University

Title

An ODE associated to the Ricci flow

Ricci flow and associated techniques have played pivotal roles in solving some long-standing open problems in Geometry and Topology in recent times. In this talk we will discuss some properties of an ODE related to the evolution of curvature along the Ricci flow and my recent results in this context.

Date/Time

Venue

Mathematics Seminar Room

Speaker

Amit kumar

Affiliation

Research scholar, SMS, NISER

Title

Operator ideals

The concept of Operator Ideals will be explained through examples and several properties. These objects first occurred in the famous work ``The Memoirs'' of A. Grothendieck published in 1955. Since then, it has taken form of a vast theory of Operator Ideals.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Dr. Rohit Dilip Holkar

Affiliation

IISER Pune

Title

Locally free actions of groupoids and proper correspondences

Date/Time

Venue

Seminar Hall, SMS

Speaker

Abhrojyoti Sen

Affiliation

SMS, NISER

Title

Vanishing Pressure Limit For a Non-strictly Hyperbolic System

In this talk we will be discussing about vanishing pressure limit for the equation

u_t + (u^2/2)_x = 0

ρ_t + (ρu)_x = 0,

with initial data

u(x, 0) = u_0(x),

ρ(x, 0) = ρ_0(x),

where u is the velocity component and ρ is the density component. This equation is considered as one of the model for the large scale structure formation of universe. In this direction we find some partial results for Reimann type initial data.

Date/Time

Venue

Mathematics Seminar Room

Speaker

Pradipta Bandyopadhyaya

Affiliation

Indian Statistical Institute, Kolkata

Title

On Lindenstrauss spaces

Date/Time

Venue

SMS seminar room

Speaker

Prof. Debashis Mondal

Affiliation

Oregon State University

Title

H-likelihood methods in spatial statistics

Recent decades have witnessed significant growth and progress in spatial statistics, with applications in agriculture, epidemiology, geology, image analysis and other areas of environmental science. In recent years, new perspectives have emerged in connecting Gaussian Markov random fields with geostatistical models, and in advancing vast statistical computations. This series of lectures will focus on basic theory and computations of spatial statistics. Topics will include conditional and intrinsic autoregressions, connections between Markov random fields and geostatistics, variogram calculations, h-likelihood methods and matrix-free computations. Applications from agricultural variety trials, environmental sciences and geographical epidemiology will be discussed.

Date/Time

Venue

LH -5 Library Building

Speaker

Pofessor B V Rao

Affiliation

Chennai Mathematical Institute

Title

BROWNIAN MOTION

**Abstract:**

We undertake journey, starting with `pollen particles' of

Robert Brown to `stock prices' of Louis Bachelier to

`suspended particles' of Albert Einstein to `mathematics'

of Norbert Wiener to `random walk' view of Monroe Donsker

and enter the `stochastic calculus' Kiyosi Ito, a garden

with beautiful flowers.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Dr. Shibananda Biswas

Affiliation

Indian Institute of Science Education and Research Kolkata

Title

Reducing submodules of Hilbert modules with an invariant kernel

We show that $\mathcal H$, with an $\mathfrak S_n$ invariant reproducing kernel $K$on an $\mathfrak S_n$ domain in $\C^n$, splits into reducing submodules $\mathbb P_{\bl p} \m H$, over the invariant ring $\C[\boldsymbol z]^{\mathfrak S_n}$, indexed by the partitions $\bl p$ of $n$. We then discuss the problem of minimality, inequivalence and realization of the submodules $\mathbb P_{\bl p} \m H$, particularly in the case when $\mathcal H$ is the weighted Bergman space $\mb A^{(\lambda)}(\mb D^n)$, for $\lambda>0$. One way to deal with the equivalence problem is through the realization and for which an analogue of Chevalley-Shephard-Todd Theorem for $\mathfrak S_n$ in the analytic setup seems quintessential. In fact, we show that the analytic version do exist for the most general version, that is, for finite pseudo-reflection groups. These results are from the joint works with Swarnendu Datta, Gargi Ghosh, Gadadhar Misra and Subrata Shyam Roy.

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Mr. Archisman Bhattacharjee

Affiliation

SMS, NISER

Title

Unimodular rows and its uses to prove Quillen–Suslin theorem

* Abstract:* In the first half of the talk we define unimodular rows over a ring R and see some of its basic properties. The completability of such unimodular rows can be viewed in terms of some special multiplicative subgroups of the matrix ring over R. In the second half, we define projective modules. Free modules are projective. In 1976 Quillen-Suslin gave a sufficient condition under which the converse is true. The completability of unimodular rows over certain polynomial rings plays an important role to show the fact that finitely generated projective modules over such ring are free.

Date/Time

Venue

Online

Speaker

Dr. Rupam Karmakar

Affiliation

Chennai Mathematical Institute, India

Title

Positive cones of cycles and Seshadri constants on certain projective varieties.

**Abstract**: In the first part of the talk I will talk about nef cones of divisors and pseudo-effective cones of k-cycles on products of projective bundles over curves. In the 2nd part, I will present some results about the Seshadri constants of ample line bundles on various blow-ups of projective spaces.

Date/Time

Venue

LH-301

Speaker

Dr. Atish Sahu

Affiliation

Nagaland University SASRD, Medziphema

Title

Construction of Neighbor Balanced designs

Spatial heterogeneity in terms of trends or periodicity in blocks may affect the outcome of experiments, especially in agricultural experiments. The conventional randomized allocation of treatments to plots in a block may result in lesser precision. It has been commonly found that the experimental units which are neighbouring to each other within a block are correlated, or there may be existing significant trends even within small block. Use of some methods of local control, called spatial or nearest neighbour (NN) methods for analyzing the observations in the presence of significant trends in adjacent plots of field data, help in increasing precision. Other approaches to guard the effects from neighbouring plots in experimental designs leads to construction of useful optimal neighbour balanced block designs which are not only efficient under standard intra-block incomplete block design type analysis but also provide protection against the effects of correlated observations or potentially unknown trends which are highly correlated with plot positions within blocks (Keifer and Wynn, 1981, Cheng, 1983; Stroup and Mulitze, 1991; Jackroux, 1998 etc). Neighbour balanced designs are designs, wherein the allocation of treatments is such that every treatment occurs equally often with every other treatment as immediate neighbours. All Ordered Neighbour design (AONBD) are those designs where allocation of treatments is done such a way that neighbor balance is obtained at every order of neighbor, given immediate neighbor is first order.

Date/Time

Venue

LH 4

Speaker

Vijay Kumar Sohani

Affiliation

IISc Bangalore

Title

Nonlinear Schrodinger equation and Hardy Sobolev inequality for the twisted Laplacian

In this talk we will see the well posedness results for the nonlinear Schr\"{o}dinger equation for the magnetic Laplacian on $\R^{2n}$, corresponding to constant magnetic field, namely the twisted Laplacian on $\C^n$ with power type nonlinearity $\lambda |u|^{\alpha} u$. We establish the well posedness in certain first order Sobolev spaces associated to the twisted Laplacian. The approach is via the spectral theory of the Schr\"{o}dinger propagator for the twisted Laplacian, and local existence is proved using Strichartz estimates established for the same.Using blowup analysis and conservation laws, we conclude global well posedness in the defocussing case (\lambda>0) with $0\leq \alpha< 2/(n-1)$ and also in the focussing case (\lambda<0) with $0\leq \alpha< 2/n$.We also prove finite time blow up in the focussing case (\lambda<0) with $2/n\leq \alpha< 2/(n-1)$. In this talk we also see a Hardy-Sobolev inequality for the twisted Laplacian on $\C^n$. We also show that the inequality is optimal in the sense that weight can not be improved.

Date/Time

Venue

Mathematics Seminar Room

Speaker

Alladi Sitaram

Affiliation

ISI, Bangalore

Title

The importance of Complex Analysis-2

Date/Time

Venue

Conference Room, School of Mathematical Sciences

Speaker

Dr. Pradeep Kumar Rai

Affiliation

Bar-Ilan University, Israel

Title

Order of the Schur multiplier of finite p-groups

We shall derive some bounds on the order of the Schur multiplier of finite p-groups. We shall also classify finite p-groups having Schur multiplier of maximum order. Finally we shall discuss the Schur multiplier and covering groups of special p-groups having derived subgroup of maximum order.

Date/Time

Venue

SMS Seminal Hall

Speaker

Rahul Kumar Singh

Affiliation

HRI, Allahabad

Title

Maximal surfaces, Born-Infeld solitons and Ramanujan's identities

Abstract: In the first part of the talk we discuss a different formulation for describing maximal surfaces in Lorentz-Minkowski space $ \mathbb{L}^3:=(\mathbb{R}^3, dx^2+dy^2-dz^2) $ using the identification of $ \mathbb{R}^3 $ with $ \mathbb{C}\times \mathbb{R} $. This description of maximal surfaces help us to give a different proof of the singular Bj\"orling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surfaces which contain a given closed real analytic spacelike curve and has a special singularity. In the next part we make an observation that the maximal surface equation and Born-Infeld equation (which arises in physics in the context of nonlinear electrodynamics) are related by a Wick rotation. We shall also show that a Born-Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. Finally in the last part of the talk we show the connection of maximal surfaces to analytic number theory through certain Ramanujan’s identities.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Aprameyan Parthasarathy

Affiliation

Universität Paderborn

Title

Boundary values, resonances and scattering poles on rank one symmetric spaces

In this talk, we will report on recent work (with J. Hilgert and S. Hansen, Paderborn) relating resonances and scattering poles on Riemannian symmetric spaces of rank one. We use boundary values in the sense of Kashiwara and Oshima to show that resonances and scattering poles coincide, along with their residues. Our methods also enable us to give a new and simple proof of the Helgason's conjecture in the rank one case. Time permitting, we'll mention progress made for symmetric spaces of higher rank.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Karen Strung

Affiliation

Radboud University - Radboud University

Title

C*-algebras, Dynamical Systems, and Classification

Simple unital nuclear C*-algebras, assuming a minor finiteness condition and the so-called UCT, can be classified up to *-homomorphisms by an invariant consisting of K-theory, traces, and a pairing between these objects. I will discuss the classification of such C*-algebras by focussing on the classification for C*-algebras arising from two interesting classes of dynamical systems: minimal homeomorphisms with mean dimension zero and mixing Smale spaces.In my fist lecture I will introduce the classification programme as well as the construction of C*-algebra from dynamical systems via crossed products and groupoids.In my second lecture, I will discuss properties and detail the classification of the two classes mentioned above.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Bidyut Sanki

Affiliation

IMSc, Chennai

Title

Graphs of systoles on hyperbolic surfaces

In this talk, we study the configuration of systoles (minimum length geodesics) on closed hyperbolic surfaces. The set of all systoles forms a graph on the surface, in fact a so-called fat graph, which we call the systolic graph. We study which fat graphs are systolic graphs for some surfaces, we call these admissible. There is a natural necessary condition on such graphs, which we call combinatorial admissibility. Our first result characterizes admissibility. It follows that a sub-graph of an admissible graph is admissible. Our second major result is that there are infinitely many minimal non-admissible fat graphs (in contrast, to the classical result that there are only two minimal non-planar graphs).

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Anish Ghosh

Affiliation

TIFR Mumbai

Title

Effectivity in arithmetic and dynamics

The first talk will be a leisurely introduction to dynamics of group actions on homogeneous spaces of Lie groups.

Date/Time

Venue

SMS Seminar Hall

Speaker

Ms. Archana S

Affiliation

NISER

Title

Transformation groups

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Mr. A S Abdul Shabeer

Affiliation

SMS, NISER

Title

Plücker Formula

*Abstract:* Plücker Formula gives the genus of a smooth projective plane curve in terms of its degree, specifically, a curve of degree d has genus (d-1)(d-2)/2. We will first prove Bezout's theorem and as an application look at Plücker formula.

Date/Time

Venue

Online

Speaker

Mr. Ajith Kumar T.

Affiliation

SMS, NISER

Title

Weak Solutions of Elliptic Boundary Value Problems.

Abstract: In this talk, we will discuss the existence of weak solutions for some elliptic boundary value problems. In particular, we will discuss the weak solutions corresponding to the Laplace operator and the Biharmonic operator.

Date/Time

Venue

LH-301

Speaker

Anindya Ghatak

Affiliation

NISER, Bhubaneswar

Title

Order theoretic properties in $C^*$ algebra and its generalisation

Date/Time

Venue

M1

Speaker

Professor Rahul Roy

Affiliation

Indian Statistical Institute, New Delhi

Title

Rank of random matrices (continuation of last seminar)

Date/Time

Venue

SMS seminar hall

Speaker

Sudarshan Kumar

Affiliation

University of Concepcion, Chile

Title

On conservation laws with discontinuous flux

Conservation laws with discontinuous flux appears in the models of two phase flow in porous media, traffic flow with discontinuous road surface, clarifier thickener models of continuous sedimentation, enhanced oil recovery process etc. In this talk we begin with an introduction to both theoretical and numerical aspects of scalar conservation laws with discontinuous flux (CL-DF)[1, 2, 4, 6]. Apart from the basic difficulties for the mathematical analysis, this discussion include the convergence analysis of a second order scheme to the physically relevant (entropy) solution[3]. We continue the discussion with the applications of CL-DF to the system of non strictly hyperbolic partial differential equations, where we propose an efficient numerical method which overcomes the difficulties in the discretization [7]. Together with the stability analysis, this method is applied to a system of equations which models the multicomponent polymer flooding problem of enhanced oil recovery process. In the latter half we discuss a high order numerical method of discontinuous Galerkin scheme applied to a coupled two phase flow-transport problem in the context of discontinuous flux [5]. Apart from this, prior to the summary and future work we discuss about the instability issue which arises in the Buckley-Leverett problem[8].References[1] Adimurthi, J. Jaffre, G. D. Veerappa Gowda, Godunov-type methods for conservation laws with a flux function discontinuous in space, SIAM J. Numer. Anal. 42(2004) 179-208.[2] Adimurthi, G. D. Veerappa Gowda, Conservation laws with discontinuous flux, J.Math. Kyoto Univ. 43 (1) (2003) 27-70.[3] Adimurthi, K. Sudarshan Kumar, G. D. Veerappa Gowda, Second order schemefor scalar conservation laws with discontinuous flux, App. Numer. Math. 80 (2014)46-64.[4] R. B¨urger, K.H. Karlsen, J.D. Towers, An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections, SIAM J. Numer.Anal. 47 (2009), 1684-1712.[5] R. B¨urger, S. Kumar, K. Sudarshan Kumar, R. Ruiz-Baier, Discontinuous approximation of viscous two phase flow in heterogeneous porous media, J. Comput.Phys. 321 (2016), 126-150.[6] T. Gimse, N. H. Risebro, Solution of the Cauchy Problem for a conservation lawwith discontinuous flux function, SIAM J. Math. Anal. 23 (1992), 635-648.[7] K. Sudarshan Kumar, C. Praveen, G.D. Veerappa Gowda, A finite volume methodfor a two-phase multicomponent polymer flooding, J. Comput. Phys. 275 (2014)667–695.[8] H. P. Langtangen, A. Tveito, R. Winther, Instability of Buckley-Leverett Flow ina Heterogeneous Medium, Transp. Porous Media, 9 (1992) 165-185.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Dr. Md. Ali Zinna

Affiliation

Ramakrishna Mission Vivekananda University

Title

Some results on the orbit space of unimodular row

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Ami Viselter

Affiliation

University of Haifa, Israel

Title

Locally compact quantum groups: the von Neumann algebraic approach-1

Lecture series abstract: We will survey the von Neumann algebraic approach to locally compact quantum groups in the sense of Kustermans and Vaes, roughly following the treatment by Van Daele. We will begin with an intro to the theory of weights of von Neumann algebras. We will then proceed to describe locally compact quantum groups. If there is any time left, we will present some recent progress in the field. The prerequisite for attending the talks is some basic knowledge of C*-algebras (and perhaps also von Neumann algebras, depending on the audience).

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Kunal Krishna Mukherjee

Affiliation

IIT Madras

Title

Factoriality of q-deformed Araki-Woods algebras

We discuss factoriality and structural properties of the q-deformed algebras of Hiai. These are type III cousins of the free group factors, extremely complicated objects and even very basic questions about them remain open. Using maximal abelian subalgebras we demonstrate that they are factors except few cases - the problem being open since 2000.

Date/Time

Venue

SMS, Seminar Room

Speaker

Rajat Subhra Hazra

Affiliation

Indian Statistical Institute, Kolkata

Title

Mathematical Background of Random Graphs

Abstract: This is an informal talk on Random graphs and its relation to complex analysis. NB: This talk is organized as a part of ongoing "Advanced Instructional School on Stochastic Processes". Please note the unusual timing.

Date/Time

Venue

Seminar Hall

Speaker

Ashutosh Nanda

Affiliation

SMS, NISER

Title

Cryptographical Significant Boolean function

Date/Time

Venue

Mathematics Seminar Room

Speaker

Anindya Ghatak

Affiliation

NISER

Title

Quantization of $A_{0}(K)$-spaces and $M$-ideals in matrix ordered spaces

Abstract: The theory of $M$-ideals in Banach spaces as well as in operator spaces is one of the important areas of research. It is well known from the literature that order structures and compact convex sets play a significant role in this area. Especially, the characterization of $M$-ideals in $A(K)$-spaces in terms of split face of the compact convex set $K$, established by Anderson and Alfsen, is a classical theorem of great importance.In this thesis, we have characterized $M$-ideal in order smooth $\infty$-normed spaces in terms of split faces of the quasi-state spaces. Also, we discuss the complete $M$-ideals in matricially order smooth $\infty$-normed spaces. For $p\neq \infty$, we introduce the notion of ideals, smooth $p$-order ideals to initiate the study of ideals in order smooth $p$-normedspaces.We introduce the notion of an $L^{1}$-matrix convex set in $*$-locally convex space. We show that $\{A_{0}(K_{n}, M_{n}(E))\}$(the `quantized functional space’) is a $\mathrm{C}^*$-ordered operator space. Conversely, every $\mathrm{C}^*$-ordered operator space is complete isometrically, completely isomorphic to $\{A_{0}(Q_{n}(V) M_{n}(V))\}$, where $Q_{n}(V)$ is the quasi-state space of $M_{n}(V)$ (in the matrix duality).

Date/Time

Venue

Seminar room

Speaker

Ranadip Gangopadhyay

Affiliation

Banaras Hindu University

Title

A Study on Few Non-Riemannian Curvatures in Riemann-Finsler Spaces

In this talk, I shall discuss some basic definitions and examples of Finsler geometry. Afterthat I shall talk about some special Finsler metrics such as Kropina change of m-th rootmetrics, Finsler spaces with rational spray coeffiecients, the general (α, β) Finsler metricsand some of their non-Riemannian curvature properties.

Date/Time

Venue

SMS Conference Room (via GoogleMeet)

Speaker

Satish Pandey

Affiliation

Technion - Israel Institute of Technology

Title

Entanglement breaking rank and quantum majorization

In Quantum Information Theory, quantum states and quantum channels are central objects of study. Mathematically, a quantum state is a positive semidefinite matrix of unit trace, and a quantum channel is formalized by a linear map which is completely positive and trace preserving (CPTP).

In the first part of this talk, we describe a rank function, that we call the ``entanglement breaking rank", of a special class of quantum channels called ``entanglement breaking channels". We show how this rank parameter for a particular channel links to one of the most celebrated problems in frame theory, commonly referred to as Zauner's conjecture. This helps us present an analytic, perturbative approach to the conjecture rather than algebraic. This part of the talk is based on a joint work with Vern Paulsen, Jitendra Prakash (NISER alumnus), and Mizanur Rahaman.

In the second part of this talk, we discuss an ordering of quantum states referred to as ``quantum majorization'', which is a natural generalization of the concept of matrix majorization in the quantum mechanical setting. We shall briefly revisit the work by Gour et al. (Nature Communications, 2018); they established a characterization for majorization of quantum states in the finite-dimensional setting via the notion of conditional min-entropy. We then outline our work where we extend the characterization by Gour et al. to the context of semifinite von Neumann algebras. Our method relies on a connection between the conditional min-entropy and the operator space projective tensor norm for injective von Neumann algebras. This part of the talk is based on a joint work with Priyanga Ganesan (NISER alumnus), Li Gao, and Sarah Plosker.

Date/Time

Venue

Vertual

Speaker

Prem Nigam kar

Affiliation

NISER

Title

JB algebras

Thursday, November 25 · 4:00 – 5:00pm

Google Meet joining info

Video call link: https://meet.google.com/jfd-idsz-eho

Or dial: (US) +1 484-531-2784 PIN: 449 578 389#

Date/Time

Venue

LH-101

Speaker

Professor S. G. Dani

Affiliation

T.I.F.R and I.I.T. Bombay

Title

Lattice points in regions of the plane and spaces of higher dimension

**Abstract: **Lattice points contained in regions of the plane, and higher dimensional Euclidean spaces, have been a topic of much study, going back at least to the century-old work of Minkowski. In recent decades there have been many developments in the general area, with many new insights brought in. The talk will aim at giving a flavour of the ideas involved, at a rudimentary level.

**Tea:** 3.30 p.m

Date/Time

Venue

LH 301

Speaker

Dr. Sumit Mohanty

Affiliation

IIT Kanpur

Title

Maximization of Combinatorial Schrodinger Operator's Smallest Eigenvalue with Dirichlet Boundary Condition

For a nonnegative potential function q and a given locally finite graph G, we study thecombinatorial Schr¨odinger operator Lq(G) = ∆G + q with Dirichlet boundary condition on aproper finite subset S of the vertex set of G such that the induced subgraph on S is connected.Let Υp = {q ∈ Lp(S) : q(x) ≥ 0, Px ∈Sqp(x) ≤ 1}, for 1 ≤ p < ∞. We prove the existenceand uniqueness of the maximizer of the smallest Dirichlet eigenvalue of Lq(G), whenever thepotential function q ∈ Υp. Furthermore, we also establish the analogue of the Euler-Lagrangeequation on graphs.

Date/Time

Venue

M-4

Speaker

Prof. B. Sury

Affiliation

Indian Statistical Institute, Bangalore

Title

Polynomials, Primes and Progressions

Abstract: Hilbert noted that the polynomial x^4 - 10 x^2 + 1 is irreducible over the integers whereas it is reducible modulo all primes. What is behind this? If two polynomials f,g with integer coefficients take the same set of values modulo all primes, what is the relation between f and g? What proportion of primes divide numbers of the form 2^n + 1? How many of these are of the form 4m+3? What about primes dividing 7^n + 12^n in some arithmetic progression? Are there infinitely many prime numbers such that the decimal expansion of 1/p recurs with period p-1? Given an integer a, if every prime dividing a^n-1 for some n also divides b^n-1, is b necessarily a power of a? We discuss the interesting mathematics behind such questions.

Date/Time

Venue

Seminar Hall (SMS)

Speaker

Dibyendu Roy

Affiliation

IIT, Kharagpur

Title

Fault analysis and weak key-IV attack on Sprout and constructions of T-function

This talk basically consists of two parts. First is, attacks on the stream cipher 'Sprout' and the second is, constructions of T-function, which carries good cryptographic properties.The design Specification of Sprout was proposed at FSE, 2015. Firstly, I will discuss about fault attack on Sprout then I will talk about the weak key-IV pairs of the same cipher. The second part of my talk deals with a new and interesting cryptographic primitive known as 'T-function', which was introduced by Klimov and Shamir in 2003. I will discuss its construction along with its various properties.

Date/Time

Venue

Mathematics Seminar Hall

Speaker

Vaibhav Pandey

Affiliation

NISER alumnus

Title

Some weirdly well behaving rings

We consider certain rings of smooth functions on a nice space, like a circle, and try to explore its algebraic nature using the smoothness of these functions. As a motivation for this, recall the ring C[0,1] of continuous real valued function on [0,1]. Recall how we prove that its maximal ideals (algebraic structure) are points using the compactness (topological structure) of [0,1].Only basic knowledge of ring theory and analytic functions is required, however, even these 2 topics will be revised in the beginning of the talk.

Date/Time

Venue

SMS seminar Hall

Speaker

Bhargab Chattopadhyay

Affiliation

IIIT Vadodara

Title

Generalized Gini Index based on U-statistics

Gini index (G), a scaled version of Gini’s mean difference (GMD), is a U-statistic of degree two. In this presentation, I will present a general approach to construct a new class of inequality measures called ad-hoc inequality measures (AIM) which are based on U-statistics of degree higher than two. The new AIMs satisfy anonymity, scale invariance, and population independence.We illustrate situations where delicate internal features with income disparities are more clearly explained and motivated from elementary economic persuasions of population dynamics, but those delicate features may be incorrectly missed by G. That is, one or more newly proposed AIMs are more apt to capture intricatefeatures than G in some instances. Without assuming any specific nature of the population distribution for the data, we have derived (i) the asymptotic mean square error of a general AIM; and also (ii) the asymptotic distribution of AIM: These results have provided useful inference methodologies which have beensupplemented with extensive sets of simulations and analyses of real economic data.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Satyajit Guin

Affiliation

IISER Mohali

Title

Noncommutative complex and Kähler geometry

Noncommutative generalisation of complex and Kähler manifolds was proposed and studied by Fröhlich-Grandjean-Recknagel. In this talk, I shall discuss a class of examples of such objects coming from C*-dynamical systems with invariant trace.

Date/Time

Venue

SMS Conference Hall

Speaker

Sabyasachi Dey

Affiliation

IIT Madras

Title

Some results on Stream Ciphers

Date/Time

Venue

M1

Speaker

Mr. Puspendu Pradhan

Title

Blocking sets of certain line sets to an elliptic quadric in PG(3,q)

Date/Time

Venue

SMS seminar room

Speaker

Dr. Nabin Kumar Meher

Affiliation

NISER, PDF

Title

Transcendence of Hurwitz zeta type series and related questions

Abstract: In this talk, we discuss the transcendence of special values of some Hurwitzzeta type series. Moreover, we find a linear independence criteria of these series undersome mild conditions. We also show that, for any a, b ∈ (0, 1) ∩ Q with a + b = 1, atleastone of the ζ(2k, a) or ζ(2k, b) must be transcendental.

Date/Time

Venue

SMS Seminar Hall

Speaker

A S Abdul Shabeer

Affiliation

SMS, NISER

Title

Hurwitz's Formula for Compact Riemann Surfaces.

Given a holomorphic map between compact Riemann surfaces, Hurwitz's formula relates the genera of the domain and range with the degree and ramification of the map. Hence, given two compact Riemann surfaces we get a restriction on the possible types of holomorphic maps between them. In particular, we also get the possible types of meromorphic functions on a compact Riemann surface.

Date/Time

Venue

Online: meet.google.com/jjx-swoa-yqx

Speaker

Rajeeb Ranjan Mohanta

Affiliation

Ph.D Student

Title

On complete metric approximation property for mixed q-Araki-Woods von Neumann algebras

Abstract: In this talk we will discuss the w*-complete metric approximation property for mixed q-Araki-Woods von Neumann algebras for any Q=(q_i,j)_i,j where q_i,j real numbers with max |q_i,j|<1. By adapting an ultraproduct technique of Junge and Zeng, we prove that the mixed q-Araki-Woods von Neumann algebras is isomorphic to ultraproducts of some mixed q-Gaussian and some q-Araki-Woods von Neumann algebras. As a consequence, we discuss its applicability for the completely bounded norm of radial multipliers on mixed q-Gaussian von Neumann algebras to mixed q-Araki-Woods von Nuemann algebras, hence establishing the w*-cmap for mixed q-Araki-Woods von Neumann algebras.

Date/Time

Venue

Online

Speaker

Ms. Saswati Mukherjee

Affiliation

SMS, NISER

Title

Symmetric property of solution for a 2nd order partial differential equation

**Abstract:** We show that the solution of the equation in and in is radial by using maximum principle

Date/Time

Venue

LH301

Speaker

Dr. Parashar Mohanti

Affiliation

Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur

Title

Compleletely bounded multipliers on $L^p$

Date/Time

Venue

PL-8

Speaker

Dr. Laxman Saha

Affiliation

Department of Mathematics, Balurghat College

Title

Graph Radio k-coloring Problems : Variations of Channel Assignment Problem

The Channel Assignment problem(CAP) is a general framework focused on point-to-point communication, e.g. in radio or mobile telephone networks. One of its main threads asks for an assignment of frequencies or frequency channels to transmitters while keeping interference at an acceptable level and making use of the available channels in an efficient way. Thus the main task of the channels assignment problem is to assign channels to the station in a way that avoids interference and uses spectrum as efficient as possible. Radio k-colorings of graphs is a variation of channels assignment problem. For a simple connected graph G with diameter q, and an integer k, 1 6 k 6 q, a radio k-coloring of G is an assignment f of non-negative integers to the vertices of G such that |f (u) − f (v)| > k + 1 − d(u, v) for each pair of distinct vertices u and v of G, where d(u, v) is the distance between u and v in G. The span of a radio k-coloring f , rck (f ), is the maximum integer assigned by it to some vertex of G. The radio k-chromatic number, rck (G) of G is min{rck (f )}, where the minimum is taken over all possible radio k-colorings f of G. For k = q and k = q − 1 the radio k-chromatic number of G is termed as the radio number (rn(G)) and antipodal number (ac(G)) of G respectively. Radio k-chromatic number is known for very limited families of graphs and specific values of k (e.g. k = q, q − 1, q − 2).For this research talk only we discuss the results which are related to the radio number of graphs. For an n-vertex graph G, we shall discuss about a lower bound of rn(G) which depends on a parameter based on a Hamiltonian path in a metric closure Gc (an n-vertex complete weighted graph where weight of an edge uv is dG (u, v)). Using this result we show that how we can derive lower bounds of rn(Cn ), rn(Pm Pn ), rn(Cm Cn ), rn(Cm Pn ) and rn(Km Cn ). For any tree T an improved lower bound of radio number depending on maximum weight Hamiltonian path of T have been shown. Next we discuss about an upper bound of rn(G) by giving a coloring scheme that works for general graph and depends on the partition of the vertex set V (G) into two partite sets satisfying some conditions. We investigate the radio number of power of cycles (C r ), Toroidal Grids Tm,n. We present an algorithm which gives a radio coloring of a graph G. For an n-vertex graph the running time of this algorithm is O(n4 ).

Date/Time

Venue

M5

Speaker

Buddhananda Banerjee

Affiliation

IISER Kolkata

Title

Linear Increment in Efficiency with the Inclusion of Surrogate Endpoint

Surrogate end-points are used when the true end-points are costly or time consuming.In a typical set up we observe a fixed proportion of true-and-surrogateresponses, and the remaining proportion are only-surrogate responses. It is obviousthat the inclusion of such only-surrogate end-points increase the efficiency ofassociated estimation. In this present paper we want to quantify the gain in efficiencyas a function of the proportion of available true responses. Also we obtain theexpression of the gain in true sample size at the expense of surrogates to achieve afixed power, as a function of the proportion of true responses. We present ourdiscussion in the two-treatment set up in the context of odds ratio.

Date/Time

Venue

SMS seminar hall

Speaker

Soma Maity

Affiliation

Ramkrishna Mission Vivekananda University, Belur.

Title

ON THE STABILITY OF Lp-NORMS OF RIEMANNIAN CURVATURE AND ON WILKING’S CRITERION FOR RICCI FLOW

Let M be a compact manifold without boundary. One can define a smooth real valued function of the space of Riemannian metrics of M by taking Lp-norm of Riemannian curvature for p ≥ 2. Compact irreducible locally symmetric spaces are critical metrics for this functional. I will show that rank 1 symmetric spaces are local minima for this functional by studying stability of the same at those metrics. I will also exhibit examples of symmetric metrics which are not local minima for it. In the 2nd part of my talk I will talk about Wilking’s criterion for Ricci Flow. B Wilking has recently shown that one can associate a Ricci flow invariant cone of curvature operators C(S), which are nonnegative in a suitable sense, to every AdSO(n,C) invariant subset S ⊂ so(n,C). We show that if S is an AdSO(n,C) invariant subset of so(n, C) such that S ∪ {0} is closed and C+(S) ⊂ C(S) denotes the cone of curvature operators which are positive in the appropriate sense then one of the two possibilities holds: (a) The connected sum of any two Riemannian manifolds with curvature operators in C+(S) also admits a metric with curvature operator in C+(S) (b) The normalized Ricci flow on any compact Riemannian manifold M with curvature operator in C+(S) converges to a metric of constant positive sectional curvature.

Date/Time

Venue

SMS Seminar Hall

Speaker

Prof. Bart De Bruyn

Affiliation

Ghent University, Belgium

Title

Finite Fields

This will be the third lecture of a series of five on Finite Fields.

Date/Time

Venue

SMS Seminar Room

Speaker

Antar Bandyopadhyay

Affiliation

Indian Statistical Institute, New Delhi

Title

De-Preferential Attachment Random Graphs

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Vaibhav Vaish

Affiliation

ISI Bangalore

Title

Punctual gluing of t-structures and the motivic intersection complex of Shimura varieties

We formalize a simple minded notion of ``punctual gluing'' of t-structures which is nevertheless powerful enough to streamline or improve several relative motivic constructions in the literature. Examples include that of relative Artin motive, relative Picard motive, relative analogue of Bondarko's weight structure or the relative motivic t-structure on (compact) 1-motives.As a completely novel construction, we recover analogue of certain S.Morel's weight truncations in the motivic setting. As an application we can construct the analogue of an intersection complex for an arbitrary threefold in (Voevodsky's) triangulated category of mixed motives. Even more strongly, for several Shimura varieties (including all Shimura threefolds, most Shimura fourfolds, the Siegel six fold) we can construct the intersection motive in the category of relative Chow motives.

Date/Time

Venue

SMS seminar room

Speaker

Anirvan Chakraborty

Affiliation

Ecole Polytechnique Federale de Lausanne, Switzerland

Title

Introduction to Functional Data Analysis

Functional Data Analysis is one of the frontline areas of research in statistics. The field has grown considerably mainly due to the plethora of data types that cannot be handled and analyzed by using conventional multivariate statistical techniques. Such data are very common in areas of meteorology, chemometrics, biomedical sciences, linguistics, finance etc .The lecture series will primarily aim at introducing the field of functional data analysis. Since functional data analysis is broadly defined as the statistical analysis of data, which are in the form of curves or functions, we will start with probability distributions and random elements in infinite dimensional Hilbert spaces, concepts of mean and covariance kernel/operator, the associated Karhunen-Loeve expansion and some standard limit theorems in Hilbert spaces. We will then discuss some selected statistical inference problems involving functional data like inference for mean and covariance operators, functional principal component analysis, functional linear models, classification problem with functional data, robust inference techniques for functional data etc. We will recall some results from functional analysis as and when required during the lectures.

Date/Time

Venue

SMS Conference Hall

Speaker

Saswata Adhikari

Affiliation

NISER

Title

Hardy and Sobolev type inequalities associated with Grushin and Dunkl operators

Date/Time

Venue

SMS Seminar Room

Speaker

Yasuyuki Kawahigashi

Affiliation

University of Tokyo

Title

Conformal field theory and operator algebras: lecture-3

I will present interactions among 2-dimensional conformal field theory, which is a kind of quantum field theory in physics, theory of operator algebras and the Moonshine conjecture which predicted mysterious relations between the finite simple group Monster and the elliptic modular function. I will emphasize representation theoretic aspects and do not assume anyknowledge of these theories.

Date/Time

Venue

Conference Room, School of Mathematical Sciences

Speaker

Dr. Ranjan Kumar Das

Affiliation

IIT Guwahati

Title

Solving rational eigenvalue problems through strong linearizations.

Rational matrices G(x) arise in many applications such as in vibration analysis of machines, buildings, and vehicles, in control theory and linear systems theory and as approximate solutions of other nonlinear eigenvalue problems. The spectral data (poles, zeros, eigenvalues, eigenvectors, minimal bases, and minimal indices) of G(x) play a vital role in many applications. In this talk, we propose the definition of Rosenbrock strong linearization of rational matrices: by a Rosenbrock strong linearization of a rational matrix G(x) we mean a matrix pencil L(x) preferably of smallest dimension that reveals the pole-zero structure of G(x). Then we construct a family of pencils (which we refer to as GFPRs) of G(x) and show that GFPRs are Rosenbrock strong linearizations of G(x). Moreover, we show that GFPRs of G(x) is a rich source of structure-preserving linearizations of G(x) and utilize these pencils to construct structure-preserving Rosenbrock strong linearizations of structured (symmetric, skew-symmetric, even and odd) rational matrices G(x). Finally, we describe the recovery of eigenvectors, minimal bases, and minimal indices of G(x) from those of the GFPRs.

Date/Time

Venue

Online (Google Meet)

Speaker

Abhishek Das

Affiliation

Tata Institute of Fundamental Research, Centre for Applicable Mathematics

Title

Analysis of the initial value problem for two specific non-strictly hyperbolic systems

Date/Time

Venue

SMS Conference Room

Speaker

Mr. Abhrojyoti Sen.

Affiliation

SMS, NISER

Title

Solutions in the class of measures for some hyperbolic systems of conservation laws and scalar conservation laws with discontinuous flux.

This talk will be focused on the non-classical solutions to some hyperbolic systems of conservation laws and scalar conservation laws with discontinuous flux. We use the method of vanishing pressure limit and vanishing viscosity limit to construct solutions. For scalar conservation laws with discontinuous flux, we propose a generalized weak solution based on the vanishing viscosity limit. We then introduce a numerical scheme for this scalar conservation law that effectively captures the solution and we also do its convergence analysis. Next, we establish a Hopf-Lax type formula for the solution to the initial-boundary value problem for the 1D pressureless gas dynamics model by introducing generalized potentials.

Date/Time

Venue

LH-101

Speaker

Rajula Srivastava

Affiliation

NISER, Bhubaneswar

Title

Tree t spanners in 2 connected outerplanar graph

Date/Time

Venue

LH 301

Speaker

Dr. Sachin S. Sharma

Affiliation

TIFR, Mumbai

Title

Integrable modules for Lie tori

Centerless Lie tori play an important role in explicitly constructing the extended affine Lie algebras; they play similar role as derived algebras modulo center play in the realization of affine Kac-Moody algebras. In this talk we consider the universal central extension of a centerless Lie torus and classify its irreducible integrable modules when the center acts non-trivially. They turn out to be highest weight modules for the direct sum of finitely many affine Lie algebras upto an automorphism.

Date/Time

Venue

SMS, Seminar Room

Speaker

Abhash Kumar Jha

Affiliation

NISER, Bhubaneswar

Title

THE ADJOINT OF SOME LINEAR MAPS COSTRUCTED USING RANKIN-COHEN BRACKETS AND SPECIAL VALUES OF CERTAIN DIRICHLET SERIES

**Abstract**: Modular forms are important objects in number theory and it has a wide range of applications in all other branches of Mathematics as well as in Physics. A modular for has Fourier expansion and the Fourier coefficients determine the modular form. Dirichlet series (e.g.,Riemann Zeta function) are important objects in number theory, used to study the distribution and properties of primes. Certain special values of Dirichlet series appears as Fourier coefficients of modular form. Kohnen [1991] constructed certain cusp forms whose Fourier coefficients involve special values of certain Dirichlet series of Rankin type by computing the adjoint map w.r.t. the Petersson scalar product of the product map by a fixed cusp form. Using differential operators one can define certain bilinear operators called the Rankin-Cohen brackets which is generalization of product. Recently the work of Kohnen has been generalized by Herrero [2015], where the author computed the adjoint of the map constructed using Rankin-Cohen brackets instead of product by a fixed cusp form. Fourier coefficients of the image of a cusp form under the adjoint map involves special values of certain Dirichlet series of Rankin-Selberg type similar to the one which appeared in the product case with certain twisting arising from binomial coefficients appearing in the Rankin-Cohen bracket. The work of Kohnen has been generalised to other automorphic forms (e.g., Jacobi forms, Siegel modular forms, Hilbert modular forms etc.,). Rankin-Cohen brackets for Jacobi forms and Siegel modular forms of genus two were studied by Choie explicitly using certain differential operators. Therefore it is natural to ask, how one can extend the work of Herrero to the case of Jacobi forms and Siegel modular forms of genus 2. A part of the thesis discuss about these generalizations. We shall also discuss the similar generaliza- tion for the case of half integral weight modular forms developed by Shimura [1973] and as a consequence, we get non-vanishing of certain Rankin- Selberg type Dirichlet series associated with modular forms. We shall also see how our method can be used to give a different proof of Rankin’s method in case of certain automorphic forms.

*NB: This is a Thesis Colloquium/Open **Seminar, School of Mathematical Sciences, NISER-Bhubaneswar.*

Date/Time

Venue

Seminar Hall, Mathematics Department.

Speaker

Dr. Ritwik Mukherjee

Affiliation

School of Mathematical Sciences, NISER Bhubaneswar.

Title

Introduction to Smooth Manifolds

This is a planned series of informal lectures, where we develop the theory of smooth manifolds. We will start from scratch keeping prerequisites to a bare minimum.

Date/Time

Venue

Mathematics Seminar Hall

Speaker

Ritwik Mukherjee

Affiliation

NISER

Title

A few methods to compute De-Rham cohomology

We will discuss some methods to compute the De-Rham Cohomology of smooth manifolds. We will discuss how to apply Mayer-Vietoris (which is the analogue of Van-Kampen Theorem for (co)homology).

Date/Time

Venue

SMS seminar hall

Speaker

Satyaki Mazumder

Affiliation

IISER Kolkata

Title

Bayesian analysis of one dimensional chirp signal

Chirp signals are frequently used in different areas of science and engineering. MCMCbased Bayesian inference is done here for purpose of one step and multiple step prediction incase of one dimensional single chirp signal with i.i.d. error structure as well as dependenterror structure with exponentially decaying covariances. We use Gibbs sampling techniqueand random walk MCMC to update the parameters. We perform five simulationstudies for illustration purpose. We also do some real data analysis to show how the methodis working in practice.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Sagnik Sen

Affiliation

Rama Krishna Mission Vivekananda University

Title

Graph homorphisms and colorings

In this talk, we will see how the notion of graph homomorphism generalizes the concept of coloring and help defining parameters such as clique number, independence number, chromatic number etc. for different types of graphs, such as, oriented graphs, signed graphs, colored mixed graphs etc.More importantly, we will see how these new concepts and works relate itself to the popularly known theories.

Date/Time

Venue

Mathematics Seminar Room

Speaker

Jitendra Prakash

Affiliation

Waterloo University USA

Title

Entanglement breaking rank

Abstract: In this talk, we shall introduce the notion of a "quantum channel" and then define a special class of quantum channels called "entanglement breaking channels". For a map in this special class, we shall define what we mean by its entanglement breaking rank. We shall show how this rank parameter for a certain map links to an open problem in linear algebra: Zauner's conjecture. The prerequisites for this talk will be minimal with some background in linear algebra, and will be aimed towards students.

Date/Time

Venue

Seminar Hall

Speaker

Dr. Varun Thakre

Affiliation

International Centre for Theoretical Sciences (ICTS-TIFR), Bengaluru (India)

Title

Generalised Seiberg-Witten equations and de-generate metrics

Abstract: Gauge theories, which have their origin in physics, have had a profound effect on mathematics and nowhere is it more strikingly evident than in dimension four. Seiberg-Witten equations and Seiberg-Witten invariants have proven to be powerful instruments for the study of smooth structures on four-manifolds.

In my talk, I will introduce the equations and talk about a generalisation of the same. Almost all the well-known gauge theories on four-manifolds can be treated as special case of this generalisation. I will then discuss some of my latest results that show an interesting pattern, in which a class of such gauge theories on four-manifolds can be thought of as statements about de-generate metrics. I will then discuss some consequences of this observation and end the talk with some research directions I plan to pursue.

Date/Time

Venue

Seminar Room, School of Mathematical Sciences

Speaker

Chitrabhanu Chaudhuri

Affiliation

IISER Pune

Title

Topological results on Moduli of Curves

First I shall introduce the moduli space of curves over complex numbers.This has been a central object of study in Algebraic Geometry with connections in mathematical physics, number theory and complex dynamics. This is also the primary object of study in my research. I shall then talk about a stratification of the moduli space by affine varieties and mention some partial results in this direction. Changing topics I shall then talk about more recent work on some moduli spaces of elliptic curves with applications to number theory.

Date/Time

Venue

SMS Conference Room

Speaker

Surojit Ghosh

Affiliation

University of Haifa

Title

Higher differentials in Adams spectral sequence

The E_2-term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for other Bousfield-Kan types spectral sequence. In this talk, I'll explain how the higher terms of such spectral sequences are determined by truncations of functors, defined in terms of certain (spectrally) enriched functor called mapping algebras. This is joint work with David Blanc.

Date/Time

Venue

Online (GoogleMeet)

Speaker

Samir Shukla

Affiliation

IIT Bombay

Title

Neighbourhood complexes of graphs

Date/Time