Search Talks

In this talk, we will understand the concept of multi-threading, a common technique to speed up computation by parallelizing it on multiple cores in a computer. We will also understand some interesting problems that arise when synchronizing across multiple threads in a program, using simple puzzle-like examples.

We stand on the brink of many rapid advancements in the field of computational linguistics and natural language processing, and arguably one of the most important has been the development of large language models. While the availability of data and increases in computational power have played a crucial role in the development of these models, they do not learn language in the same way as a human child. Nevertheless, they excel at learning fairly complex grammatical knowledge in several languages. This often leads to public opinion that says, the problem of machines learning language has been 'solved'. In this talk I discuss why this idea might be premature, highlighting some recent research on these topics.

Human activities have considerably altered biodiversity as well as the ecological processes underlying these patterns, resulting in both local and region-wide extinction. Birds, a diverse taxon, have offered a valuable opportunity to understand how biodiversity responds to climate change, habitat alterations and ecological degradation. Based on over 25 years of experience working on the problem of bird species survival in human-dominated landscapes, in varied geographies such as Sariska Tiger Reserve, Corbett Landscape and the Western Himalayas, Ghazala Shahabuddin will discuss the process of field-based ecological research: from natural history observations, hypothesis development, data collection and analysis and drawing inferences from ecological data. She will especially delve into the features that distinguish ecological research from lab-based science. She will discuss not only the difficulties of ecology, but equally, the joys of field-based ecology, that can be as rewarding as it is challenging.

This popular talk will focus not only on the beautiful lens that mathematics provides to study and model innumerable things but also on the immense effectiveness in providing applications.
The idea is to immerse the listener into the world of mathematics. We will touch upon symmetry and art, applications of mathematics to medicine, and time permitting a glimpse of its use in cryptography.

In this largely non-technical talk, I shall discuss the importance of probability theory as a discipline, describe some fundamental results and questions of interest, and provide some historical context.

Dazzling dance of a peacock, vocal repertoires of a nightingale, seismic signals of a wolf spider are breathtaking examples male display to woo their respective females. In some cases, males also fight, form leks, commit ‘suicide’ or ‘cheat’ to mate with the females. In this talk we will look at such diverse varieties of behaviors seen in nature, that is driven by sexual selection.

A famous question of Greenberg (which was also formulated independently by Coleman) asks the following:
Suppose p is a prime and f is a p-ordinary modular eigenform of weight at least 2. If the restriction of the p-adic Galois representation attached to f to the local Galois group at p splits into a direct sum of two characters, then does f have complex multiplication?
In this talk, we will explore an analogue of this question in the setting of Siegel modular forms of genus 2.
This talk is based on a joint work in progress with Bharathwaj Palvannan.

We discuss new applications of some "zeta elements" which form Kolyvagin systems. A portion of this talk originated from discussions with Minhyong Kim, and another portion is joint work in progress with Gyujin Oh.

I will introduce via examples, and then state and prove generalizations of Chen's cross ratios theorem on the special values of Rankin-Selberg L-functions for GL(n) x GL(m). I will then discuss applications of this theorem to Deligne's conjecture on the special values of various automorphic L-functions. This talk is a report of an ongoing collaboration with Harald Grobner, Michael Harris, and Jie Lin.

Let p \geq 5 be a prime. We construct a lattice in a self-dual modular Galois representation for which the p-torsion of the corresponding Bloch-Kato Selmer group is arbitrarily large. This extends the work of Matsuno for elliptic curves and small primes. Our representation is constructed by appropriately modifying an argument of Hamblen and Ramakrishna which allows one to lift reducible mod p Galois representations to characteristic zero with local conditions at a prescribed set of primes. This talk is based on recent joint work with Anwesh Ray (https://arxiv.org/pdf/2504.16287).

Let E/F be an elliptic curve with CM by an imaginary quadratic field K, and assume that the extension of F generated by the torsion points of E is abelian over K. In this talk I will outline the proof of the p-part of the Birch-Swinnerton-Dyer formula for E in analytic rank 1 for primes p>3 of ordinary reduction. For F=Q, this was originally proved by Rubin in 1991 as a consequence of his proof of the Iwasawa main conjecture for K. In contrast, our approach to the problem is based on the study of an auxiliary Rankin-Selberg convolution, and extends to CM abelian varieties A/K and higher weight CM modular forms.

I will explain the theory of Kolyvagin systems of Gauss sum type (or of rank 0) for certain self-dual representations over a number field. I especially discuss a remarkable, decisive property of the systems for the structure of Selmer groups, based on joint work with R. Sakamoto.