Mathematics Colloquium
Speaker: Bhaswar B. Bhattacharya (Associate Professor, University of Pennsylvania)
Host: Parthanil Roy
Title: Higher-Order Graphon Theory: Fluctuations, Inference, and Degeneracies
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, August 06
Venue: Ramanujan Hall
Abstract: Motifs (patterns of subgraphs), such as edges and triangles, encode important structural information about the geometry of a network. Consequently, counting motifs in a large network is an important statistical and computational problem. In this talk we will consider the problem of estimating motif densities and fluctuations of subgraph counts in an inhomogeneous random graph sampled from a graphon. We will show that the limiting distributions of subgraph counts can be Gaussian or non-Gaussian, depending on a notion of regularity of subgraphs with respect to the graphon. Using these results and a novel multiplier bootstrap for graphons, we will construct joint confidence sets for the motif densities. Finally, we will discuss various structure theorems and open questions about degeneracies of the limiting distribution and connections to quasirandom graphs. (Joint work with Anirban Chatterjee, Soham Dan, and Svante Janson)

Number theory seminar
Speaker: Hariom Sharma (IIT Roorkee)
Host: Ravi Raghunathan
Title: On representations of $GL(n,D)$ with a symplectic model
Time, day and date: 10:00:00 AM - 11:00:00 AM, Thursday, August 07
Venue: online (https://meet.google.com/pqd-fyod-xqi)
Abstract: Let $F$ be a non-Archimedean local field of characteristic zero, and let $D$ be the unique quaternion division algebra over $F$. For $n \in \mathbb{N}$, let $G_n = GL(n,D)$. The subgroup $H_n = Sp(n,D)$ of $G_n$ denotes the unique non-split inner form of the symplectic group $Sp(2n, F)$.
A smooth admissible complex representation $(\pi,V)$ of $G_n$ is said to have a symplectic model (or to be $H_n$-distinguished) if there exists a non-zero linear functional $\phi$ on $V$ such that $\phi(\pi(h)v) = \phi(v)$ for all $h \in H_n$ and $v \in V$.
In this talk, we provide a complete list of irreducible admissible representations of $G_3$ and $G_4$ having a symplectic model. We demonstrate that induced representations from finite-length representations preserve the symplectic model. Furthermore, we classify those ladder representations of $G_n$ that admit a symplectic model. In addition, we prove a part of Prasad's conjecture which provides a family of irreducible unitary representations with a symplectic model.

Commutative Algebra seminar
Speaker: Tony Puthenpurakal (IIT Bombay)
Title: Lyubeznik's theory of F-modules-I
Time, day and date: 4:00:00 PM - 5:00:00 PM, Thursday, August 07
Venue: Ramanujan Hall
Abstract: In the first lecture we show Kunz result that if $R$ is regular of characteristic $p > 0$ then the Frobenius is flat. We also define F-modules introduced by Lyubeznik.

Speaker: Subho Majumdar (Head of AI at VIJIL, a US-based startup)

Host: Radhendushka Srivastava

Date: 8 Aug 2025

Time: 3:00 to 4:00 pm

Venue: Ramanujan Hall

Title: Towards Statistical Foundations for Reliable and Defendable Large
Language Models

Abstract: The emergence of Large Language Models (LLMs) has brought in
concomitant concerns about the security and reliability of generative AI
systems. While LLMs promise powerful capabilities in diverse real-world
applications, ensuring that their outputs are resilient to malicious
attacks and consistent across similar inputs has significant methodological
and computational challenges. This situation calls for the revisiting of
modern deep learning architectures through a statistical lens.

I will present on two interconnected themes in this area. First, I will
introduce Representation Noising (RepNoise), a defense mechanism that
protects the weights of open-source LLMs against malicious uses. RepNoise
achieves this through controlled noise injection in the knowledge
representations inside a model that makes it harder to recover harmful
information later. Second, I will discuss my work on the consistency
problem—the equivalent of robustness in LLMs concerned with measuring and
minimizing the sensitivity of LLM outputs to input variations through a
combination of controlled synthetic data generation and fine-tuning.

I will conclude by discussing ongoing work at the intersection of AI
security and statistics, including the development of statistical bounds
for the strength of defense mechanisms like RepNoise, and robustness
frameworks for ensuring AI system reliability in high-stakes applications.
 

Partial Differential Equations seminar
Speaker: Vikram Giri (ETH Zurich)
Host: Harsha Hutridurga
Title: Non-uniqueness for the transport equation with incompressible Sobolev vector fields
Time, day and date: 4:00:00 PM - 5:00:00 PM, Friday, August 08
Venue: Ramanujan Hall
Abstract: After recalling the DiPerna-Lions theory for the transport equation with Sobolev vector fields, we will review recent works that construct non-unique solutions using convex integration techniques.

Commutative Algebra seminar
Speaker: Vaibhav Pandey (Purdue University, West Lafayette, USA)
Host: Sudhir R. Ghorpade
Title: The optimal number of equations needed to define a variety: Connections with invariant theory
Time, day and date: 5:0:00 PM – 6:00:00 PM, Friday, August 08
Venue: Ramanujan Hall
Abstract: The arithmetic rank of a variety is the smallest number of equations needed to define it, i.e., the number of hypersurfaces needed to cut out the given variety. In general, this number turns out to be notoriously difficult to compute.

This talk will shed light on the interplay between classical and modern techniques in algebra. We will begin with a quick introduction to classical invariant theory and its role in laying some of the groundwork for modern algebra. We will focus on the classical representations of linear algebraic groups and explicitly compute the arithmetic ranks of their `nullcone variety' (introduced by Hilbert) in all characteristics.

This is ongoing work with Jack Jeffries, Anurag Singh, and Uli Walther.