Finite Geometry and Coding Theory Seminar
Speaker: Puspendu Pradhan, IIT Bombay
Host: Sudhir R. Ghorpade
Title: PGL_2(q)-orbits of lines of PG(3,q) and Higher weight spectra of some Reed-Muller codes
Time, day and date: 11:30:00 AM - 12:15:00 PM, Monday, September 29
Venue: Ramanujan Hall
Abstract: (https://drive.google.com/open?id=1mASoUTg688KdSHa7n-RVYKl51v32qIb8)
We shall divide the talk into two parts. In the first part, we focus on the problem of classifying the lines of the projective 3 space PG(3, q) over a finite field Fq into orbits under the action of the group PGL2(q), which represents the linear symmetries of the twisted cubic C. While this problem has been addressed in the literature for characteristic 2, in this talk we shall consider the case of characteristic 6= 2. We reduce this question to the classification of binary quartic forms over Fq into PGL2(q)-orbits. This part of the talk is based on joint works with Krishna Kaipa and Nupur Patanker. For non-negative integers ν and m, the Reed–Muller code RMq(ν, m) is defined as the subspace obtained by evaluating all polynomials of degree at most ν in m variables, with coefficients in Fq, at the points of the affine space AG(m, q). In the second part of the talk, we will present progress on determining the higher weight spectra of the Reed–Muller code RMq(2, 3) over the ternary field F3. This part of the talk is based on an ongoing joint work with Sudhir Ghorpade, Trygve Johnsen, Rati Ludhani, and Rakhi Pratihar.

APS
Speaker: Chayan Karmakar, IIT Bombay
Host: Ravi Raghunathan
Title: Geometry of the Tensor Product for SL(3,C)
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, September 29
Venue: Ramanujan Hall
Abstract: We aim to study the geometric structure of tensor products of irreducible representations of $\mathrm{SL}(3, \mathbb{C})$. By plotting the highest weights of the irreducible components in the weight lattice, we observe that they form some convex regions. We also study additional structural properties of the tensor products, including a stability result in the resulting tensor diagrams

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

Google Meet joining info
Video call link: https://meet.google.com/pqn-bnit-yqw

The talks will be broadcasted in the Ramanujan hall as well.

Towards Statistical Foundations for Reliable and Defendable Large Language Models

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.

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

Google Meet joining info
Video call link: https://meet.google.com/pqn-bnit-yqw

The talks will be broadcasted in the Ramanujan hall as well.

Towards Statistical Foundations for Reliable and Defendable Large Language Models

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.

Topology Seminar
Speaker: Sudarshan Gurjar, IIT Bombay
Title: Kodaira Embedding theorem
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, October 03
Venue: Ramanujan Hall
Abstract: The Kodaira embedding theorem is a fundamental theorem which can be viewed as a bridge between complex geometry and algebraic geometry.  It answers the question about when a compact complex manifold admits a holomorphic embedding inside complex projective space. The talk will be mostly about explaining this theorem. It will be a mix of complex geometry, algebraic geometry and topology. Basic knowledge of differential topology will be assumed