Speaker: Hari Prasadh ,IIT Bombay
Time: May 2, Tuesday at 5:15 pm
Venue: Ramanujan Hall

Title: Existence and uniqueness results for ODEs with non-smooth vector
fields

Abstract: We study the existence and uniqueness results for ordinary
differential equations with coefficients in Sobolev spaces. The
aforementioned conclusions are derived from the relevant linear transport
equation results from the seminal Diperna-Lions paper.
 

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.
 

Mathematics colloquium

Venue: Ramanujan Hall, Department of Mathematics

Speaker: Tapabrata Maiti, Michigan State University

Host: Ayan Bhattacharya

Date: Wednesday, May 17, 2023

Time: 10.00 am 

Title: Statistical Foundation of Deep Learning: Application to Big Data

Abstract: Deep learning profoundly impacts science and society due to its impressive empirical success in applying data-driven artificial intelligence. A key characteristic of deep learning is that accuracy empirically scales with the sizes of the model and the amount of training data. Over the past decade, this property has enabled dramatic improvements in state-of-the-art learning architectures across various fields. However, due to a lack of mathematical/statistical foundation, the developments are limited to specific applications and do not generalize to a broader class of highly confident applications. This lack of foundation is more evident under limited training sample regimes when applied to statistical estimation and inference. We attempt to develop statistically principled reasoning and theory to validate the application of deep learning, thereby paving the way for interpretable deep learning. Our approach builds on Bayesian statistical theory and methodology and scalable computation. We illustrate the methodology with a wide range of applications.

IPDF Talk 

Speaker: Om prakash, IIT Gandhinagar

Host: Manoj K Keshari

Date : 22nd May, Monday

Time : 4-5 pm.

Title: A Study of certain Affine Semigroups and Semigroup Rings.

Abstract: It has been proved that there is no upper bound on the Betti
numbers of a numerical semigroup ring for a fixed embedding dimension
$e\geq 4$. The same question can be asked for affine semigroup rings as
well. However, unlike numerical semigroup rings, affine semigroup rings do
not necessarily have the Cohen-Macaulay property, and the existence of
Pseudo Frobenius elements of an affine semigroup is also not guaranteed.
We will discuss some results and examples in this talk and try to show how
the Cohen-Maculayness and the pseudo-Frobenius set play an important role
in the study.

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

Statistics/Probability job talk

Date and time:  May 25, 2023 (Thursday) 3 to 4 pm

Venue: Ramanujan Hall, Department of Mathematics

Host: Murali K Srinivasan 

Speaker:   Ashish Mishra

Affiliation: UFPA, Brazil

Title: On quasi Steinberg characters of complex reflection groups

Abstract: Consider a finite group G and a prime number p dividing the order of G. A
p-regular element of G is an element whose order is coprime to p. An irreducible character
χ of G is called a quasi p-Steinberg character if χ(g) is nonzero for every p-regular element
g in G. A quasi p-Steinberg character χ is called weak p-Steinberg if χ has degree |G|p.
These variants of p-Steinberg character were introduced to answer a question of Dipendra
Prasad that asked whether the existence of a weak p-Steinberg character of G implies
that G is a finite group of Lie type. In this joint work with Digjoy Paul and Pooja Singla,
we classify quasi p-Steinberg characters of all finite irreducible complex reflection groups.
In the first part of the talk, we will give an overview of representation theory of complex
reflection groups.