Abstract: The talk will start with an introduction to the field of "Symplectic geometry".  We will see the statement and the proof outline of Gromov's non-squeezing theorem, which is one of the most important results in the field. Via the proof of this result, we will see the role played by holomorphic curves in studying symplectic manifolds.

All are cordially invited to the seminar.

Abstract:  The classical isoperimetric problem asks: among all plane regions with a fixed perimeter, which one encloses the largest area? The isoperimetric inequality answers this question quantitatively and shows the circle (and in higher dimensions, the sphere) is uniquely optimal. In three dimensions, this answers why a soap bubble tends to become spherical.

Chronic oxidative stress is implicated in a wide range of human diseases, yet its causal and tissue-specific roles in disease initiation and progression remain poorly defined. In this seminar, I will present how redox stress functions as a context-dependent driver of pathology across neurovascular, cardiovascular, maternal (preeclampsia), and metabolic(diabetes) disease states.

Venue: Room 301, Samgatha

Disease-Specific Tau Assemblies and Their Mechanisms of Cellular Propagation

The Department of Mathematics is pleased to announce a two-day symposium featuring invited talks by the following distinguished experts:

• Prof. Riddhi Shah, Jawaharlal Nehru University, Delhi

• Prof. Jaydeb Sarkar, Indian Statistical Institute, Bengaluru

Abstract: In this talk, we shall first recall the notion of integrable modules over affine Kac-Moody algebras, after developing the necessary background. We shall then introduce the concept of weakly integrable modules (in the sense of Kac-Wakimoto) and henceforth provide a complete classification of irreducible weakly integrable modules over these Lie algebras. Finally, if time permits, we shall discuss the analogous classification result for extended affine Lie algebras of nullity 2.

Abstract: Fix your favorite smooth, compact curve C in the plane. How many rational points of a prescribed denominator size are in a given neighborhood of C? In the first part of the talk, we motivate this question and discuss a simple random model predicting the answer. 

In the second part, we use (purely) analytic and geometric tools to approach the question. Special emphasis will be placed on explaining the role of the Fourier transform of the surface measure.

All are cordially invited to the seminar.