Past conference symposium workshop

Most Indian Universities however do not have a rigorous study on probability. The aim of this school is to give a comprehensive training to students in a undergraduate/PhD programme on probability and stochastic processes. Also to give them a chance to interact with researchers in these topics. This is a follow up program of last year AIS on stochastic process held here at NISER, Bhubaneswar.
We propose to run three courses – 1) Measure theoretic probability, 2) Conditional probability and Martingale, 3) Brownian motion. There will be around 30 hours of lectures including tutorials per topic over a 3 weeks period. 

Organizers:

a) Nabin Kumar Jana, Assistant Professor, NISER, Bhubaneswar

b) Rahul Roy, Professor, ISI, Delhi

Funded by: IASc, Bengaluru and NCM, Mumbai

Target audience: Those who have attended Advanced Instructional School on stochastic processes 2018.

Speakers: 
a) B V Rao, CMI, Chennai
b) Rahul Roy, ISI, Delhi
c) Parthanil Roy, ISI, Bangalore
d) Arijit Chakrabarty, ISI, Kolkata
e) Srikanth Iyar, IISc, Bangalore

f) Manjunath Krishnapur, IISc, Bangalore

Syllabus: We plan to cover the following topics in this AIS.

1. Measure theoretic probability: Caratheodory extension theorem , Monotone class theorem, Dynkin’s pi-lambda theorem, MCT, Fatou’s Lemma, DCT, Fubini’s theorem. Probability spaces, random variables and random vectors, expected value and its properties. Independence. Various modes of convergence and their relation. The Borel-Cantelli lemmas. Weak Law of large numbers for i.i.d. finite mean case. Kolmogorov 0-1 law, Kolmogorov’s maximal inequality. Statement of Kolmogorov’s three-Series theorem (proof if time permits). Strong law of large numbers for i.i.d. case. Characteristic functions and its basic properties, inversion formula, Levy’s continuity theorem. Lindeberg CLT, CLT for i.i.d. finite variance case, Lyapunov CLT.

2. Conditional probability and Martingale: Absolute continuity and singularity of measures. Hahn-Jordon decomposition, Radon-Nikodym Theorem, Lebesgue decomposition. Conditional expectation – Definition and Properties. Regular conditional probability, proper RCP. Regular conditional distribution. Discrete parameter martingales, sub-and super-martingales. Doob’s Maximal Inequality, Upcrossing inequality, martingale convergence theorem, Lp inequality, uniformly integrable martingales, reverse martingales, Levy’s upward and downward theorems. Stopping times, Doob’s optional sampling theorem. Discrete martingale transform, Doob’s Decomposition Theorem. Applications of martingale theory: SLLN for i.i.d. random variables.

3. Brownian motion: Introduction to Brownian Motion, Kolmogorov Consistency theorem, Kolmogorov Continuity theorem, Construction of BM. Basic Martingale Properties and path properties – including Holder continuity and non-differentiability. Quadratic variation. Markov Property and strong Markov property of BM, reflection principle, Blumenthal’s 0-1 law. Distributions of first passage time and of running maximum of BM.

Interested participant can fill the following google form till 19th June 2019:

https://forms.gle/KHr4WYjxbk9gHT569

Program Schedule:

Confirmed Participants:

https://sites.google.com/a/niser.ac.in/qgrpncg

In the early days of our learning , most of our knowledge and practice of Integration is based on the Fundamental Theorem of Integral Calculus (FTIC). But the ideas and the intuition of it changes drastically as one tries to move onto higher dimensions or onto more "general sets", leading to new intuition, new Mathematics, entangling analysis with topology. In even more abstract setting, a rephrasing of FTIC leads to new theories of Integration with its "associated FTIC" . 

http://www.niser.ac.in/IWM/index.html

TBA

For more details/registration please follow the link https://sites.google.com/niser.ac.in/ncga-niser2020/home

 This will be an introductory summer school on "J-Holomrphic Curves and Gromov-Witten Invariants".We hope to cover the foundations of this subject by following the book "J-Holomorphic Curves and Symplectic Topology" by Dusa McDuff and Dietmar Salamon. Quite a few young mathematicians from India have agreed to  give lecturesin this summer school. Those who are interested in Differential Geometry, Differential Topology,   Complex Analysis and (Complex) Algebraic Geometry are particularly encouraged to participate in this programme.  The details of this summer school can be found on this website  http://www.niser.ac.in/niser_jhol/  

Most Indian Universities however do not have a rigorous study on probability. The aim of this school is to give a comprehensive training to students in a undergraduate/PhD programme onprobability and stochastic processes. Also to give them a chance to interact with researchers in these topics.
We propose to run three courses – 1) Basic probability theory, 2) Measure free Markov chain, 3)Modules of linear algebra and real analysis. There will be around 40 hours of lectures includingtutorials per topic over a 4 weeks period. In addition, over two weekends we plan to invite activeresearchers in probability to present introductory lectures on a research topic and interact withstudents.

Organizers:

a) Nabin Kumar Jana, Assistant Professor, NISER, Bhubaneswar

b) Rahul Roy, Professor, ISI, Delhi

Target audience: 3rd year of B.Sc.; 1st year of M.Sc. or 3rd & 4th year of Integrated M. Sc. students in Mathematics or Physics, 4th Year B.Tech. students in Electrical Engineering.

Speakers: Any 8 out of the following:
a) B V Rao, CMI, Chennai
b) Rahul Roy, ISI, Delhi
c) Anish Sarkar, ISI, Delhi
d) Antar Bandyapadhyay, ISI, Delhi
e) Krishanu Maulik, ISI, Kolkata
f) Parthanil Roy, ISI, Bangalore
g) Arijit Chakrabarty, ISI, Kolkata
h) Srikanth Iyar, IISc, Bangalore
i) Nabin Kumar Jana, NISER, Bhubaneswar
j) Manjunath Krishnapur, IISc, Bangalore

k) Probal Choudhuri, ISI, Kolkata

l) Alok Goswami, ISI, Kolkata

Syllabus: We plan to cover the following topics in this AIS.
Modules of Linear Algebra and Analysis:
     Linear Algebra: Vector Spaces: Denition of Vector Spaces and Subspaces, Basis of a Vector Space, Linear Equations, Vector Spaces with an Inner Product; Theory of Matrices and Determinants: Matrix Operations, Elementary Matrices and Diagonal Reduction of a Matrix, Determinants, Transformations, Generalized Inverse of a Matrix, Matrix Representation of Vector Spaces, Bases, etc., Idempotent Matrices, Special Products of Matrices; Eigenvalues and Reduction of Matrices: Classication and Transformation of Quadratic Forms, Roots of Determinantal Equations, Canonical Reduction of Matrices, Projection Operator, Further Results on g-Inverse, Restricted Eigenvalue Problem; Convex Sets in Vector Spaces: Denitions, Separation Theorems for Convex Sets

     Analysis: Metric spaces, open/closed sets, Cauchy-Schwarz Inequality, Holder's Inequality, Hadamard's Inequality, Inequalities Involving Moments, Convex Functions and Jensen's Inequality, Inequalities in Information Theory, Stirling's Approximation sequences, compactness, completeness, continuous functions and homeomorphisms, connectedness, product spaces, completeness of C[0; 1] and Lp spaces, Arzela-Ascoli theorem
    Reference Texts:
    1. C.R. Rao: Linear Statistical Inference and Its Applications.
    2. A. Ramachandra Rao and P. Bhimasankaram: Linear Algebra.
    3. G. F. Simmons: Introduction to Topology and Modern Analysis
    4. J. C. Burkill and H. Burkill: A second course in mathematical Analysis

Basic Probability Theory:
   Orientation, Elementary concepts: experiments, outcomes, sample space, events. Discrete sample spaces and probability models. Combinatorial probability and urn models; Conditional probability and independence; Random variables { discrete and continuous; Expectations, variance and moments of random variables; Transformations of univariate random variables; Jointly distributed random variables; Conditional expectation; Generating functions; Limit theorems;

    Reference Texts:
    a) S. M. Ross: A rst course in Probability
    b) Jacod & Protter: Probability Essentials
    c) W Feller: An Introduction to Probability: Theory and Its Applications, Vol I & II
    d) George G. Roussas: Introduction to Probability

Markov Chain:
Random Walk, Discrete Markov chains with countable state space. Classication of states -- recurrence, transience, periodicity. Stationary distributions, limit theorems, positive and null recurrence, ratio limit theorem, reversible chains. Several illustrations including the Gambler's ruin problem, queuing chains, birth and death chains etc. Poisson process, continuous time markov chain with countable state space, continuous time birth and death chains.

  Reference Texts:
1. W. Feller: Introduction to the Theory of Probability and its Applications, Vol. 1.
2. P.G. Hoel, S.C. Port and C.J. Stone: Introduction to Stochastic Processes.
3. S.M. Ross: Stochastic Processes.
4. S. Karlin and J. Taylor: Stochastic Processes, Vol. 1.
5. J.G. Kemeny, J.L. Snell and A.W. Knapp: Finite Markov Chains.

Last date of application is 10th May 2019.

Application form is available here.

List of selected participants:

Second List:

• To ensure the utilization of our full resources, selected participants through second list are requested to confirm their participation by 22nd May, 2019 to aissp @ niser.ac.in.
• To confirm the participation, a mail along with inwards travel documents, that is, copy of your train/bus tickets has to be send to aissp @ niser.ac.in. For local participants there is no need of any travel documents, only confirmation mail will suffice.
• For those who will travel by train, the nearest railway station from NISER, Bhubaneswar is “Khurda Road”. So book your ticket accordingly.
• Hostel accommodation from 16th June to 13th July 2019 will be provided to the participants but participants has to bring their own bedcover.
• Food (breakfast, lunch & dinner) will be served from evening of 16th June to morning of 13th July 2019. Along with the confirmation, please let us know if you have any dietary restrictions.

• Based on the reply, a Third list of selected candidates may be published on 23rd May 2019.

   

National Workshop on Cryptology-2014(under the aegis of Cryptology Research Society of India) will be held at IIITDM, Jabalpur, MP on 25-27 September 2014.
The Workshop Coordinators are Dr Sraban Mohanty, IIITDM, Jabalpur and Dr Deepak Kumar Dalai, NISER, Bhubaneswar.
Website: http://nwc.iiitdmj.ac.in/

School of mathematical Sciences is going to host AIS Harmonic Analysis (2018) Please visit  https://www.atmschools.org/2018/ais/ha  for details of the programme.

https://sites.google.com/iith.ac.in/decemberworkshop/

Abstract: We shall discuss Euclid's problem of trying to derive the parallel postulate from the remaining axioms.