Title: Spectral sequence 
Speaker: Bittu Singh. 
Abstract: we'll see how exact couple appear. Then discuss few properties. How
spectral sequence stabilizes under some minor hypothesis. Then using serrey's
spectral sequence we'll compute homology group of some spaces.

Speaker: Eric Urban, Columbia University

Host: Dipendra Prasad

Title: Congruences and modular forms

Abstract: The observation that there exist congruences between modular forms go back to the early works of Ramanujan. I will describe some aspect of the implications of their existence in arithmetic. Prof Urban is among leading number theorists in the world, in particular on Iwasawa theory, and the main conjectures.

Date and Time: Wednesday, May 10, 2023, at 10.30 am

Google Meet Link: meet.google.com/zod-rqkm-giu

Speaker: Kalyan Barman, Post-doctoral Fellow, IIT Madras

Title: The Title of my Talk is: “ Stable Approximation by
Stein’s Method”

Abstract:  Probability approximation is one of the basic theories in the literature of probability theory. It has wide range of applications in limit theorems, and various field of statistics. Stein’s method is one of the most popular technique studying approximation problems. In this talk, We discuss stable distributions in the context of Stein’s method. We discuss and unify the Stein identity for stable random variables available in the existing literature. We discuss the solution of stable Stein equation via semigroup approach. Further, we discuss error bounds for stable approximations, and also obtain rates of convergence results. Finally, We will show that the optimal convergence rate in the generalized central limit theorem can be obtained using our Stein’s method setup.

Venue: Ramanujan Hall, Mathematics Department

 Speaker: Luigi Accardi

 Affiliation: University of Rome Tor Vergata, Italy

 Date and time: 4.15 pm, Wednesday, May 10, 2023

 Talk link: meet.google.com/tss-oqhb-yop

 Title: Quantum Probability: a short historical survey of the main new ideas

 Abstract: Goal of my talk to put in historical perspective the
developments that, starting from 1974 have lead to a complete
clarification of all the so-called paradoxes of quantum mechanics and of
all the apparent mysteries that surrounded this discipline since its
origins. The path leading to this clarification has been long and
tortuous, but now we know that what physicists call quantization is a very
special case of a much wider and far reaching construction which naturally
arises (i.e. without any artificial, ad hoc, construction) from the
combination of classical probability with the theory of orthogonal
polynomials.
My talk will be an extremely short synthesis of the salient moments of
this path.
 

IPDF Talk
Date and Time: Thursday, May 11, 2023, at 11.30 am

Google Meet Link: meet.google.com/rgk-afbq-fwg

Speaker: Subrata Golui, Research Scholar, IIT Guwahati

Title: Discrete-time Zero-Sum Games for Markov Chains with risk-sensitive
average cost criterion

Abstract:   We study zero-sum stochastic games for controlled discrete
time Markov chains with risk-sensitive average cost criteria with
countable state space and Borel action spaces. The payoff function is
nonnegative and possibly unbounded. Under a certain Lyapunov-type
stability assumption on the dynamics, we establish the existence of the
value and a saddle point equilibrium. Using the stochastic representation
of the principal eigenfunction of the associated optimality equation, we
completely characterize all possible saddle point strategies in the class
of stationary Markov strategies. Also, we present and analyze an
illustrative example.

IPDF Talk

Date and time:  May 11, Thursday, 4-5pm

Venue:  Link : https://meet.google.com/gyb-jfbn-oiu?authuser=0

Host: Manoj K Keshari

Speaker:  Rajib Sarkar

Affiliation: TIFR Mumbai

Title:Algebraic and homological invariants of binomial edge ideals of graphs.

Abstract:  

Let $G$ be a finite simple graph and $J_G$ be its binomial edge
ideal in the corresponding polynomial ring. Complete intersection binomial
edge ideals are characterized, and they are the paths only. In the first
half, we will discuss almost complete intersection binomial edge ideals and
their Rees algebra. Also, we will discuss the Castelnuovo-Mumford
regularity of powers of almost complete intersection binomial edge ideals.
It is also known that $J_G$ is Gorenstein if and only if $G$ is a path.
There are two natural generalizations of Gorenstein rings: level rings and
pseudo-Gorenstein rings. In the next half, we will study the levelness and
pseudo-Gorensteinness of binomial edge ideals.

CACAAG seminar

Speaker: Ayush Tewari.

Affiliation: Ghent University.

Venue: Ramanujan Hall.

Time: 5 pm, 11 May, Thursday.

Title: Dressian and metric tree arrangements.

Abstract - We give an introduction to the study of the Dressian
Dr(k,n), a tropical prevariety that is an outer approximation to the
tropical Grassmannian. We will discuss the various structures that
this space is endowed with, specifically the relation to metric tree
arrangements in Dr(3,n). If time permits, we can discuss various
generalizations and applications.