**Next Seminar**

**Title:**Real Unipotent Elements in Classical Lie Groups.

**Speaker:**Krishnendu Gongopadhyay

**Affiliation:**IISER Mohali

**Date and Time:**April 08, 2021 at 03:30PM

**Venue:**Seminar Hall, Kerala School of Mathematics.

**Abstract:**Real elements are those elements in a group which are conjugate to their own inverses. Real elements appear naturally at different branches of mathematics. These elements are also known as `reversible’ elements in the literature. These elements are closely related to the so-called strongly real elements in a group which are products of two involutions. After giving a brief exposition on real elements in groups, I shall discuss classification of real unipotent elements in classical Lie groups which is part of a joint work with Chandan Maity.

**The ‘KSoM Seminar Series’ is a fortnightly seminar series usually held on Fridays at 03:30PM.**

**These lectures are usually research seminars, wherein the speakers will lecture on their recent research work.**

**Past seminars:**

Abstract: In this talk, we will introduce the Hyper Rigidity of operator systems in -algebras as a non commutative analogue of Korovkin sets in the space of continuous functions, . Also, we point out one of our recent results, and a couple of open questions along this direction.

Abstract: Let be a complex separable Hilbert space and let be the algebra of all bounded linear operators on . In this talk, we discuss about what are the linear maps which satisfy

for every unitary on .

Abstract : The -series associated to a classical modular form (of weight and level ) denoted by

where denotes the Fourier coefficient of (in its -series expansion around ) is an analytic function on the right half plane and can be analytically continued to the whole . The non-trivial zeros of this function lie inside the critical strip . The analogue (GRH) of the Riemann Hypothesis in this context states that they all lie on the critical line itself.

The following region

where is an absolute constant, is currently known to be a zero-free region for . Some aspects of this non-vanishing related to my work will be discussed in this talk. This is a joint work with Prof M Manickam and Prof V Kumar Murty

Title: An invitation to the theory of L functions

Speaker : Krishnarjun K

Affiliation : Harish Chandra Research Institute, Prayagraj(Allahabad)

Date and Time : October 23, 2020 at 03:00 p.m.

Venue : Seminar Hall, Kerala School of Mathematics

Abstract : The aim of this talk is to introduce the notion of an function and to describe a few basic properties. We shall also prove two classical theorems, one of Riemann and Dirichlet and demonstrate how techniques from complex analysis can be used to prove arithmetic results. We shall briefly touch upon current research topics of interest in the subject, if time permits.