


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 LaplaceBeltrami Operator on Noncompact Symmetric Spaces
Abstract. In this talk, we will discuss Hardy and Adams type inequalities for fractional powers of the LaplaceBeltrami 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: OkounkovVershik 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.
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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 chipfiring game on the graph. Later, we will discuss the graph theoretic analog of the AbelJacobi map and study some of its properties.