APS
Speaker: Amanpreet Singh, IIT Bombay
Host: Saurav Bhaumik
Title: Dessins d’Enfants and the Absolute Galois Group
Time, day and date: 11:30:00 AM – 12:30:00 PM, Friday, September 26
Venue: Room 113
Abstract: In this seminar, I will talk about dessins d’enfants, a special kind of bipartite graph embedded on compact connected Riemann surfaces. We will see how such a dessin d’enfant gives a Belyi pair. Using Belyi’s theorem, we will explore how the absolute Galois group of \mathbb{Q} acts on dessins d’enfants, and this action is faithful.To summarize, we will see how dessins d’enfants provide a bridge between combinatorics, topology, algebraic geometry, and number theory

APS
Speaker: Amal Das, IIT Bombay
Host: Saikat Mazumdar
Title: Hardy-Sobolev inequality with full boundary singularity and obtainability of its sharp constant
Time, day and date: 2:15:00 PM – 3:15:00 PM, Friday, September 26
Venue: Ramanujan Hall
Abstract: We will study the Hardy-Sobolev inequality with full boundary singularity and also show that the best constant is achieved by some nonzero function under some (local) geometric conditions on the boundary of the domain. This is equivalent to a variational problem, and a solution can be obtained as an extremal for this variational problem. The core issue is to show the convergence of minimizing sequence, which we will see holds, provided one is strictly below a threshold energy level given by the best Hardy-Sobolev constant in $\mathbb{R}^n_ +$.

APS
Speaker: Kshitij Sinha, IIT Bombay
Host: Harsha Hutridurga
Title: Mathematical study of few questions in quantitative homogenization
Time, day and date: 3:30:00 PM – 4:30:00 PM, Friday, September 26
Venue: Ramanujan Hall
Abstract: In this talk, we study rates in the context of periodic homogenization of parabolic problems with large lower order terms (both drift and potential). We demonstrate that the solution is a product of three terms: (i) a function of time, (ii) the ground-state of an exponential cell eigenvalue problem and (iii) the solution to a parabolic equation with zero effective drift. For the latter, we derive L^2 rates in the homogenization limit. We will also be discussing a question regarding the interior controllability of wave equations with highly oscillatory coefficients.