Combinatorics seminar

Monday, 22 January 2024, 14:30-15:30 hrs

============================

Venue: Ramanujan Hall

Host: S. Krishnan

Speaker: Hiranya Dey

Affiliation: Indian Institute of Science, Bengaluru

Title: On the sum of the entries in the character table of a finite group

Abstract: In 1961, Solomon proved that the sum of all the entries (total sum) in the character table of a finite group does not exceed the cardinality of the group. In this
talk, we will see that for symmetric groups, the total sum is asymptotically the same as
the first column sum. We will also prove that similar results hold for hyperoctahedral
groups and demihyperoctahedral groups. We will also see the generating function for total
sum for generalized symmetric groups which uses Flajolet's work on continued fractions.
This is a joint work with Arvind Ayyer and Digjoy Paul.

Annual Progress Seminar

Tuesday, January 23, 2024, 9.30-10.30

===========================

Venue: Ramanujan Hal

Host: S. Krishnan

Speaker: Umesh Shankar

Affiliation: IIT Bombay

Title: Bijective approach to enumerating permutation statistics

Lecture series on algebraic stacks
Tuesday, 23 January 2024, 11:30 AM
========================
Venue: Room 105
Host: Sudarshan Gurjar

Speaker: Nitin Nitsure
Affiliation: Bhaskaracharya Pratishthana, Pune

Title: Separated and proper morphisms of schemes

Abstract: The basic theory of separated and proper morphisms of schemes, developed by Grothendieck, is explained in Hartshorne's book  `Algebraic Geometry' chapter 2 section 4. We will look at it from the perspective of functors of points. The functorial point of view is essential for Artin's extension of the theory of such morphisms first to algebraic spaces and then to algebraic stacks, which are going to be our next topics.

Commutative Algebra Seminar

Tuesday 23 Jan 2024, 4.00-5:30 pm

=======================

Venue: Room 215

Host: Tony J. Puthenpurakal

Speaker :Tony J. Puthenpurakal

Affiliation: IIT Bombay

Title: Modules over Weyl algebras with application to local cohomology modules over polynomial rings-III

Abstract: Let $K$ be a field of characteristic zero. We study finitely generated modules over the  Weyl algebra A_n(K). We give application to local cohomology modules of K[X_1,...., X_n]

Seminar on control theory

Wednesday, 24 January, 2.30-3.30

====================

Venue: Room 105, Dept. of Mathematics

Host: Sudhir Ghorpade

Speaker: Chandrajit Bajaj

Affiliation: University of Texas at Austin, USA

Title: Optimized Decision-Making via Active Learning of  Stochastic Hamiltonians

Abstract: A Hamiltonian represents the energy of a dynamical system in phase space with coordinates of position and momentum. Hamilton’s equations of motion are obtainable as coupled symplectic differential equations.  In this talk, I shall show how optimized decision-making (action sequences) can be obtained via a reinforcement learning problem wherein the agent interacts with the unknown environment to simultaneously learn a Hamiltonian surrogate and the optimal action sequences using Hamilton dynamics, by invoking the Pontryagin Maximum Principle. We use optimal control theory to define an optimal control gradient flow, which guides the reinforcement learning process of the agent to progressively optimize the Hamiltonian while simultaneously converging to the optimal action sequence. Extensions to stochastic Hamiltonians leading to stochastic action sequences and the free-energy principle shall also be discussed.

This is joint work with Taemin Heo, Minh Nguyen 
Brief Bio: Professor Chandrajit Bajaj is a Computational Applied Mathematics Chair in Visualization at the Department of Computer Science and the Oden Institute of Computational Engineering and Sciences at the University of Texas at Austin, USA. He is a Fellow of AAAS, ACM. IEEE and SIAM. More information about him is available at: http://www.cs.utexas.edu/~bajaj

Probability and Statistics seminar

Wednesday, 24 January, 3.00-4.00 pm 

=======================

Venue: Ramanujan Hall

Speaker: Hira Koul

Affiliation: Professor, Department of Statistics and Probability, Michigan State University

Distinguished Visiting Professor, Department of Mathematics, IIT Bombay

Title:  A signed-rank estimator in nonlinear regression models when covariates and errors are dependent

Abstract: This talk will describe the asymptotic uniform linearity of a signed rank statistic of the residuals in a class of nonlinear parametric regression models when regression errors are possibly dependent on the covariates. This result is used to prove the asymptotic normality of a signed rank estimator of the regression parameter vector in the given nonlinear regression model where covariates and regression errors are dependent. The latter result in turn is used to derive the asymptotic distribution of this signed rank estimator in the errors in variables linear regression model. The asymptotic relative efficiency of this SR estimator relative to the bias-corrected least squares estimator is shown to increase to infinity, as the measurement error variance increases to infinity, thereby establishing another robustness property of this estimator.

Venue: Ramanujan Hall

Host: Sudhir R Ghorpade 

Speaker: S K Jain

Affiliation: Ohio University, Athens, OH, USA

DATE: Wednesday, January 24 at 4 pm.