Probability and Statistics Seminar
Speaker: Dr Matthew Parry, Associate Professor in Statistics, University of Otago, New Zealand
Host: Siuli Mukhopadhyay
Title: Finding Things in High Dimensions
Time, day and date: 12:00:00 PM – 1:00:00 PM, Monday, September 28
Venue: Ramanujan Hall 
Abstract: Data scientists and statisticians look for meaningful patterns in data. But finding those patterns can become surprisingly difficult when data have hundreds, thousands, or even millions of dimensions. In this talk, I'll explore how we can group documents and images, find biomarkers for disease, and recommend movies and TV series to viewers.

Special Talk
Speaker: Prof. R.V Gurjar
Host: Krishnan Sivasubramanian
Title: The Jacobian Problem
Time, day and date: 3:00:00 PM – 4:00:00 PM, Monday, September 28
Venue: LH 302
Abstract: Recently, Alpoge, Matthew, and Claude Fable gave a surprising counterexample to the Jacobian Problem in three or more variables. In this lecture we will first start with easy observations about the Jacobian Problem. Later we will discuss interesting special results proved by many mathematicians like S.S. Abhyankar, Abhyankar Gurjar Inversion Formula, Applegate-Onishi, Bass-Connell-Wright, Jagzev, T. T. Moh, A. Magnus, Nakai-Baba, S. Wang, S. Kaliman etc. Due to lack of time no proofs will be discussed. We will suggest possible special results for young mathematicians to try to prove. We will discuss results by many mathematicians for the 2-variable Jacobian Problem.

APS
Speaker: Kshitij Sinha, IIT Bombay
Host: Harsha Hutridurga
Title: Spectral Problems and Fine Properties of Solutions in Periodic Homogenization
Time, day and date: 4:30:00 PM – 5:30:00 PM, Monday, September 28
Venue: Ramanujan Hall
Abstract: In this talk, I will discuss spectral problems for the Laplacian and the Bilaplacian in perforated domains with various boundary conditions, as well as fine properties of solutions to divergence-form elliptic PDEs, in the context of quasi-periodic and almost-periodic homogenization.

First, I will present theoretical results on the asymptotic behaviour of eigenvalues of the Bilaplacian, motivated by a work of Nandakumaran. Next, I will discuss a numerical study of the Neumann eigenvalues of the Laplacian in perforated domains, motivated by a work of Vanninathan. Finally, I will derive doubling inequalities for divergence form elliptic equations with quasi-periodic and almost-periodic coefficients.

APS
Speaker: Aditya Dwivedi, IIT Bombay
Host: Manoj K Keshari
Title: A cotriple perspective on the HKR theorem
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, September 28
Venue: Room 113
Abstract: The Hochschild-Kostant-Rosenberg (HKR) theorem states that for a smooth commutative algebra A over a field k, the Hochschild homology of A is isomorphic to the exterior powers of the module of Kahler differentials:

HHn(A,A) \iso \omega^n A/k.

In this talk I will present a cotriple perspective on this result. The free-forgetful adjunction between commutative k-algebras and k-modules gives rise to a cotriple resolution of A by polynomial algebras, and applying the Hochschild complex levelwise produces a first-quadrant spectral sequence converging to HH*(A,A). Its E2-page is given by the homology of the exterior powers of the cotangent complex, so the HKR isomorphism is equivalent to the vanishing of the higher Andre-Quillen homology of A.This forces the spectral sequence to collapse at E2, recovering the HKR isomorphism and making explicit the role of smoothness in the proof.

Plancherel Measure
Speaker: Devadatta Hegde, School of Mathematics, TIFR
Host: Ravi Raghunathan
Title:  Plancherel measure for $p$-adic groups following Harish-Chandra
Time, day and date: 5:00:00 PM – 6 :15:00 PM, Monday, September 28
Venue: Room 215
Abstract: -

APS
Speaker: Lal Bahadur Sahu, IIT Bombay
Host: Sandip Singh
Title: Some infinite families of arithmetic symplectic hypergeometric groups.
Time, day and date: 10:00:00 AM – 11:00:00 AM, Tuesday, September 29
Venue: Room 215
Abstract: In this talk, we construct some of the very first examples of infinite families of arithmetic symplectic hypergeometric groups that do NOT satisfy the arithmeticity criterion of Singh and Venkataramana.
For example, we show that the hypergeometric groups associated to the pairs of polynomials $(x-1)^4P_m(x^{9})$ and $(x^4+x^3+2x^2+x+1)Q_m(x^{9})$, where $P_m$ and $Q_m$ are integral polynomials of degree $2m$ such that the corresponding pair determines a Zariski dense symplectic hypergeometric group, are arithmetic in $\Sp(18m+4)$ for any integer $m\in\N$.

APS
Speaker: Adarsh Gupta, IIT Bombay
Host: Sudarshan R. Gurjar
Title: Line bundle restrictions to Hyperplane sections and their connections to first homology on Affine Varieties.
Time, day and date: 12:30:00 PM – 1:30:00 PM, Tuesday, September 29
Venue: Room 105
Abstract: The broad aim of the talk is to understand line bundles on affine varieties and their restrictions to hyperplane sections. We examine connections between torsion line bundles and units in the coordinate ring and also make connections of these objects with the first homology groups.

APS
Speaker: Amal Das, IIT Bombay
Host: Saikat Mazumdar
Title: Compactness and Stability for the Hardy-Sobolev equation.
Time, day and date: 2:30:00 PM – 3:30:00 PM, Tuesday, September 29
Venue: Ramanujan Hall
Abstract: We will study the Hardy-Sobolev equation with full boundary singularities and critical growth. We will show that blow-up solutions concentrate at a finite number of points on the boundary of the domain, and also show the compactness and stability of the solutions.

APS
Speaker: Amanpreet Singh, IIT Bombay
Host: Saurav Bhaumik
Title: Moduli Field Vs. Field of Definition of projective schemes over $\mathb{C}$
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, September 29
Venue: Ramanujan Hall
Abstract: In this seminar, we study the moduli field $M(X)$ of projective schemes $X$ and the question of when a projective scheme can be defined over a finite extension of its moduli field.
we study this question for projective schemes whose canonical sheaf is ample or anti-ample, and prove the following main theorem: Let $X$  be a smooth, irreducible projective scheme of finite type over $\mathbb{C}$ and the canonical sheaf $\omega_X$ or the anti-canonical sheaf $\omega_X^{-1}$ is ample, then X can be defined over a finite extension of its moduli field M(X). 
As an immediate consequence, we recover the theorem of Hammer and Herrlich: a smooth projective curve over $\mathbb{C}$ of genus $g \geq  2$ can be defined over a finite extension of its moduli field.

APS
Speaker: Pallab Kumar Sinha, IIT Bombay
Host: Siuli Mukhopadhyay
Title: Discrete Time Chain Binomial Model for Infectious Disease Transmission.
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, September 29
Venue: Conference Room
Abstract: -

APS
Speaker: Pooja Lamba, IIT Bombay
Host: Monika Bhattacharjee
Title: -
Time, day and date: 11:30:00 AM – 12:30:00 PM, Tuesday, September 29
Venue: Ramanujan Hall
Abstract: -

APS
Speaker: Sayantan Sinha, IIT Bombay
Host: Debraj Das
Title: Large Language Models, Statistics, and Watermarking 
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, September 30
Venue: Conference Room
Abstract: In this seminar presentation we examine the mathematical and statistical principles underlying modern Large Language Models (LLMs), tracing their evolution from foundational probabilistic language modeling to transformer architectures. We will also see details how classical statistical concepts including maximum likelihood estimation, scaling laws, calibration, and preference optimization empower modern training pipelines. As a primary case study, we go through rigorous mathematical analysis of statistical text watermarking, focusing on green/red list generation, logit biasing, z-statistic hypothesis testing, detection power, and robustness against editing.

Commutative Algebra seminar
Speaker: Sayed Sadiqul Islam, IIT Bombay
Host: Tony Puthenpurakal
Title: Zariski Closedness of Supports of Local Cohomology Modules
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, September 30
Venue: Room No .215
Abstract: These talks are based on two recent papers, one by Katzman and Zhang and the other by Gintz and Zhang, concerning the Zariski closedness of supports of local cohomology modules in prime characteristic.

We shall show that the support of H_I^i(R/gR) is Zariski closed when R is a regular ring of prime characteristic and g is an element R . We shall also discuss an extension of this result to the case in which R has finitely many isolated singular points. Furthermore, we shall prove that if f_1 and f_2 form a regular sequence, then the support of H_I^j(R/(f_1,f_2)) is Zariski closed.

Mathematics Colloquium
Speaker: Hemanshu Kaul, Illinois Institute of Technology
Host: Niranjan Balachandran
Title: Counting Colorings: Variations and Extensions of a theme of Kostochka and Sidorenko
Time, day and date: 4:45:00 PM - 5:45:00 PM, Wednesday, September 30
Venue: Ramanujan Hall
Abstract: In 1990, Kostochka and Sidorenko introduced the List Color Function, which counts the guaranteed number of list colorings of a given graph, as a counterpart to the classic Chromatic Polynomial, introduced by Birkhoff in 1912, which counts its ordinary colorings. They asked whether the List Color Function asymptotically equals the Chromatic Polynomial when the number of colors is large enough. This was proved by Donner (1992) with several major improvements continuing to appear till now. This phenomenon has been widely studied in the context of generalizations of ordinary colorings.
In this talk, we will discuss the history as well as some new results on this theme of Kostochka and Sidorenko: an enumerative function of (a variant of) list colorings equals the corresponding enumerative function of (the same variant of) ordinary colorings, when the number of colors is large enough. We will also see when this phenomenon fails in context of DP-colorings but can still be recovered using the Tutte polynomial.