Date: 01/07/2024 (Monday)

Time: 10am

Venue: Conference room, math office

Speaker: Dr. Anubhav Sharma

Title: Distributions of Fourier coefficients of certain Dirichlet series
under various circumstances

Abstract: In this talk, we will explore the behavior of Fourier
coefficients of certain Dirichlet series over special subsequences of
natural numbers. More precisely, we will establish asymptotic formulas for
the higher power moments related to the general divisor problem, focusing
on the coefficients of certain Rankin-Selberg $L$-functions. As a
consequence, we see a quantitative result on the number of sign changes of
these Fourier coefficients within small intervals over the same sequence.
 

Name of the Seminar: Statistics and Probability Seminar

Day, date and time: Wednesday, 24 July 2024, 4:00 pm

Venue: Ramanujan hall

Host: Debraj Das

Speaker: Mihir Dewaskar

Affiliation: Duke University

Title: Robustifying likelihoods by optimistically re-weighting data

Abstract: Likelihood-based inferences have been remarkably successful in
wide-spanning application areas. However, even after due diligence in
selecting a good model for the data at hand, there is inevitably some
amount of model misspecification: outliers, data contamination, or
inappropriate parametric assumptions such as Gaussianity mean that most
models are at best rough approximations of reality. A significant
practical concern is that under large sample sizes, even small amounts of
model misspecification may have a substantial impact on our inferences. In
this talk, we discuss how one can robustly estimate likelihood-based
models by re-weighting terms in the likelihood. We term this as
"optimistic re-weighting" because the weights are chosen to make the
re-weighted data look like that arising from our model. We describe a
theoretically motivated alternating optimization procedure called
Optimistically Weighted Likelihood (OWL) to obtain these weights. We
describe two applications of OWL: first to estimate the average treatment
effect in a micro credit study in the presence of outliers, and second to
robustly fit a Gaussian mixture model to single cell RNA-Seq data.

Speaker: Dr. Rajat Gupta
Affilitation: University of Texas at Tyler
Title: Smallest parts function of Andrews, sum-of-tails identities: A 
combinatorial excursion
Abstract: See attached PDF file

Venue: Ramanujan Hall
Time:  14:30-15:30 hrs
Date:  26th July 2024.

Title: Smallest parts function of Andrews, sum-of-tails identities: A combinatorial excursion

Abstract:  In the first half of the talk, we first review a classical combinatorial result of Ramanujan and Uchimura, which states that the difference between the sum of the smallest parts of the partitions of n into an odd number of distinct parts and the corresponding sum for an even number of distinct parts is equal to the number of divisors of n. We will see its connection with a problem arising from the theory of random acyclic graphs. The second half will be devoted to some-of-tails identities and extensions of the above theorem with its application. The works presented here are the joint work with Rahul Kumar, Noah Lebowitz-Lockard and Professor Joseph Vandehey.

Name of the Seminar: Topology Seminar (online)

Day, date and time: Friday, 26 July 2024, 2:30-3:30 PM

Venue : Google Meet joining info
Video call link: https://meet.google.com/sun-aoda-zja

Host: Rekha Santhanam

Speaker: Sumanta Das

Affiliation: IISc, Bengaluru

Title : Strong Topological Rigidity of Non-Compact Orientable surfaces.

ABSTRACT. We prove that if a homotopy equivalence between any two non-compact orientable
surfaces without boundary is a proper map, then it is properly homotopic to a homeomorphism,
provided surfaces are neither the plane nor the punctured plane.

Speaker: Agnid Banerjee

Title: Quantitative uniqueness for parabolic equations with applications

Date, Time, Venue : 30th July (Tuesday) at 11:30 am in Ramanujan Hall

Abstract: I will talk about a new sharp estimate of the order of vanishing
of solutions to parabolic equations with variable coefficients. In case of
real analytic coefficients,  I will then show that an application of such
an estimate  leads to a parabolic generalization of the well known
Donnelly-Fefferman nodal set estimate.  I will also present applications
to new Landis type results in the parabolic setting. This is based on
joint work with Vedansh Arya and Nicola Garofalo.

====================
Algebraic Groups Seminar

Tuesday, July 30, 2024, 4 pm
====================

Venue: Ramanujan Hall

Host: Shripad M. Garge.

Speaker: Dibyendu Biswas

Affiliation: IIT Bombay, Mumbai.

Title: Reductive Groups

Abstract: We start the 8th chapter of Springer's book on connected
reductive groups.

Speaker : Aranya Lahiri

Title:  Dagger groups and p-adic distribution algebras

Date, Time, Venue : 31st July (Wednesday) at 11:30 in room 215

Note that the lecture is of 90 minutes duration.

Abstract: p-adic representations of p-adic groups became central objects of
investigation especially in view of the somewhat recent p-adic Langlands
program. In this talk, I will explore how investigating the topological
irreducibility of specific p-adic principal series representations
naturally directed us to examine dagger groups linked to `*p**-saturated
groups'.* Additionally, I will discuss the curious concept of 'strict
neighborhood groups' of these p-saturated groups. Finally, I will conclude
by introducing the concept of p-adic overconvergent distribution algebras,
and arguing why they may be a more suitable candidate than their rigid
analytic counterparts for addressing certain issues in p-adic
representation theory. This is joint work with Claus Sorensen and Matthias
Strauch.

Talk 1 (Colloquium)

Speaker : Rakesh Pawar

Title: Milnor-Witt cycle modules over excellent DVR

Date, Time, Venue : 4:00 pm on Wednesday (31st July) in Ramanujan Hall

Abstract: I will briefly recall Cycle modules over a field as defined by
Rost (1996) and their significance and properties. Recently, 'modules'
over Milnor-Witt K-theory or alternatively Milnor-Witt cycle modules
over field have been formalized by N. Feld (2020).

I will talk about recent joint work with Chetan Balwe and Amit Hogadi,
where we considered the Milnor-Witt cycle modules over excellent DVR and
studied a subclass of these that satisfy certain lifting conditions on
residue maps associated with horizontal valuations. As an important
example, Milnor-Witt K-theory of fields belongs to this subclass.
Moreover, this condition is sufficient to deduce the local acyclicity
property and A^1-homotopy invariance of the associated Gersten complex.