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.