- Dr. Lakshmi Sankar (IIT Palakkad) on Analysis of PDEs
Title: Semilinear elliptic boundary value problems on unbounded domains in R^2
Abstract
We will briefly review the literature on the study of positive solutions to semilinear elliptic boundary value problems on both bounded and unbounded domains. We will then discuss our recent results establishing the existence of positive solutions for certain semilinear elliptic problems on specific unbounded domains in R^2. We will highlight the key differences that arise when working in two dimensions versus higher dimensions.
12th May, 10:15-11:15
- Dr. Ekata Saha (IIT Delhi) on Number Theory
Title: Brahmagupta-Pell equations and their variants
Abstract
The Brahmagupta-Pell equation appears in various contexts in number theory. In this talk, we will give some such examples and then discuss a few variants of this equation. Our main focus will be on the polynomial analogue of this equation. This talk will be based on joint works with Akanksha Gupta.
12th May, 11:45-12:45
- Dr. Jyoti Dasgupta (IIT Dhanbad) on Algebraic Geometry
Title: Equivariant Vector Bundles on complexity-one T-varieties
Abstract
In this talk, we explore the fascinating intersection of geometry and combinatorics,
focusing on algebraic varieties that have an added structure—the action of a torus. This
structure makes these algebraic varieties more manageable by giving them a combinatorial
description. This connection has been well-exploited in the case of toric varieties, and there
is a complete dictionary between the geometry and combinatorics of toric varieties. Toric
varieties are (normal) T-varieties of complexity zero. The next important class of Tvarieties
that one can study by combinatorial methods is that of complexity-one Tvarieties.
We give a combinatorial classification of torus equivariant vector bundles on a (normal) pro-
jective Tvariety of complexity-one. This extends the classification of equivariant line bundles
on complexity-one T-varieties by Petersen-Süb on one hand, and Klyachko’s classification
of equivariant vector bundles on toric varieties on the other hand. This is based on a joint
work with Chandranandan Gangopadhyay, Kiumars Kaveh and Christopher Manon.
12th May, 14:30-15:30
- Prof. Pallavi Dani (Louisiana State University) on Group Theory
Title: Large-scale geometry of right-angled Coxeter groups
Abstract
Right-angled Coxeter groups form an extremely accessible, yet remarkably rich class of objects in geometric group theory. They are defined by simple presentations: they are generated by involutions, with the only additional relations requiring certain pairs of generators to commute. Despite this elementary definition, they display an extraordinary range of geometric behaviors. Consequently, they have played a crucial role in the field, as a source of illuminating examples and counterexamples and as a testing ground for conjectures. In this talk, I will survey recent progress in understanding their large-scale geometry, focusing in particular on questions about quasi-isometry. Along the way, I will illustrate some of the main tools and techniques used for establishing such results, many of which are applicable in more general settings.
12th May, 19:30-20:30 (online)
- Dr. Prachi Mahajan (IIT Bombay) on Complex Analysis
Title: From One to Several Complex Variables
Abstract
In this expository talk, I will discuss how complex analysis in more than one variable is strikingly different from complex analysis in one variable. While many classical results from one-variable complex analysis admit higher-dimensional analogues, several surprising new phenomena emerge in multiple dimensions. I will introduce some of these ideas, including domains of holomorphy, Hartogs’ phenomenon, and the interplay between analysis and geometry in C^n.
13th May, 10:00-11:00 (online)
- Dr. Senthil Raani (IISER Berhampur) on Harmonic Analysis
Title: Geometry of sets of measure zero
Abstract
A famous question, asked by Falconer in 1985, "Can a large set admit a positive measure of distances?" seemingly simple is still an unsolved question connecting many areas of modern mathematics. In this talk, we begin with some of the basic concepts to understand the depth of this question that explores a guiding idea: "large sets cannot avoid geometry." These questions lead to a rich area of research that brings together Fourier analysis and geometric measure theory. The aim is to provide an accessible introduction to a rapidly developing topic that has seen significant progress over the past decade.
13th May, 11:30-12:30
