Speaker: Mithun Bhowmik, IISc Bangalore

Time & Date: 4 pm, Monday, 01 August 2022

Venue: Ramanujan Hall

Title: Hardy and Adams Type Inequalities for the Fractional Laplace-Beltrami Operator on Noncompact Symmetric Spaces  

Abstract. In this talk, we will discuss Hardy and Adams type inequalities for fractional powers of the Laplace-Beltrami operator on Riemannian symmetric space $X$ of noncompact type. We use solutions to the extension problem in combination with the ground state representation method (of Frank et al) to establish Hardy’s inequality. We will discuss $L^p - L^q$ mapping properties of the extension operator and get an improvement over the corresponding results on Euclidean spaces. This is a joint work with Sanjoy Pusti. Next, we will discuss sharp Adams type inequalities on Sobolev spaces $W^{\alpha,n/\alpha}(X)$ of any fractional order $\alpha < n$ on $X$ with dimension $n$.

DDT: Tuesday, 2 August,  2:00 – 3:30 pm

Venue : Ramanujan Hall, Department of mathematics.
Title: Okounkov-Vershik approach to the representation theory of symmetric
groups.

Abstract: In this series of talks we will bootstrap the representation
theory of symmetric groups inductively, following the 2005 revision of
Vershik's and Okounkov's seminal paper on the topic.

We have now a dedicated website where one can find the notes and resources
from the past meets and announcements of the upcoming meetings:

https://sites.google.com/view/rtag/

Please join us!

Title:  On the tensor product of representations of classical groups

Abstract: After giving a general introduction to representation theory of GL(n,C) and other classical groups, I will focus attention on Dibyendu Biswas's thesis work around the question on tensor product of representations of GL(n,C) and other classical groups.

Venue: Room No. A1A2, CDEEP, Department of Mathematics

Speaker: Rahul Karki.

Time: Friday, 5 August, 4:30 pm.

Venue: Ramanujan Hall, Mathematics department.

Title: Picard Group and Abel Jacobi Theory on A Finite Graph.

Abstract: A finite graph can be viewed, in many aspects, as a discrete version of a Riemann surface. In this talk, we will see how the notions of the Picard group and Jacobian are defined on a graph and their relations with the chip-firing game on the graph. Later, we will discuss the graph theoretic analog of the Abel-Jacobi map and study some of its properties.