+91-674-249-4082

Order structure in normed spaces and operator spaces (matricially normed spaces); Theory of operator ideals (Geometry of Banach Spaces).

Partial differential equations of evolution type, Inverse problems

Incidence Geometry, Groups, Algebraic Combinatorics

The numbers which occur in Ap\'{e}ry's proof of the irrationality of zeta(2) and zeta(3) have many interesting congruence properties.Work started with F. Beukers and D. Zagier, then extended by G. Almkvist, W. Zudilin and S. Cooper recently has complemented the Ap\'{e}ry numbers with set of sequences know as Ap\'{e}ry-like numbers which share many of the remarkable properties of the Ap\'{e}ry numbers. We study supercongruences properties of Ap\'{e}ry-like numbers.*Supercongruences:*

There are many interesting connections between differential operates and modular forms. Using Rankin-Cohen type differential operators on Jacobi forms/ Siegel modular forms we study certain arithmetic of Fourier coefficients.*Differential Operators:*

We compute convolution sums of divisor function using the theory of modular forms and quasi modular forms and apply those to find number of representations of an integer by certain quadratic forms.*Convolution sums and applications:*

**Representations of numbers by quadartic forms:**

**Specialisation: **Theoretical Computer Sciences, Coding Theory, Cryptology, Discrete Mathematics.

**Present Research Interests: **Symmetric ciphers, Algebraic Attack, Boolean Functions, Combinatorics.

Cowen-Douglas Class of operators, Hilbert modules over function algebra and Dilation theory.

Modular forms, L-functions

Transcendental number theory, Modular forms and Multiple zeta values

Combinatorics, Algebraic Graph Theory

Intersecting Families, Hypergraphs, Graph Theory, Applications of Szemer\'{e}di Regularity Lemma, Applications of analysis and probability theory to combinatorics, Probabilistic methods in combinatorics, Random graphs.

Moduli space of bundles over curves and surfaces, Linear Series.

Partial Differential Equations

Moduli of vector bundles, partial differential equations, mathematical physics, representation theory

Disordered systems pops up quite often in physics (spin glass), biology (artificial neural network), social sciences (matching) and many other places. To analyze, usually these systems are identified with the stochastic models. My main research interest is on the application of probabilistic tools to analyze these stochastic models.

My Primary research area is functional analysis and main research area is operator algebra. I study one parameter family of endomorphisms on von Neumann algebras.

I also study structure theory of von Neumann algebras, Connes's classifications theory of type III factors and various others property of type III factors and ergodic theory.

Enumerative geometry of singular curves, using methods from Differential Topology.

I work on Harmonic Analysis on Euclidean Spaces and Heisenberg Groups.

At present my research interest is Spherical harmonics, Hermite and Laguere expansion and Dunkl Transform.

I am interested to develop theory and methodologies for statistical inference with applications to real world problems. Specifically, I am interested in:

(1) Large-scale inference including multiple hypothesis testing and change point detection

(2) High-dimensional statistics, random networks

(3) Sequential Analysis: multistage and sequential procedures for hypothesis testing and interval estimation, bounded and minimum risk point estimation

(4) Stochastic processes: compound Poisson processes

Topological Quantum Groups, Operator Algebras, Noncommutative Geometry.

In general revolves around the study of Banach algebras and their multipliers associated to locally compact groups, hypergroups. In particular interested in the studies related to Fourier algebras.

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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