**Next Seminar**

Title: Noncommutative Korovkin Theory.

Speaker: Arunkumar C. S., KSoM

Date and Time: February 26, 2021 at 03:00PM

**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:**

Title: Noncommutative Korovkin Theory.

Speaker: Arunkumar C. S.

Affiliation: Kerala School of Mathematics

Date and Time: February 26, 2021 at 03:00PM

Venue: Seminar Hall, Kerala School of Mathematics

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.

Title: A certain kernel function for -values of half-integral weight Hecke eigenforms.

Speaker: Sreejith M. M.

Affiliation: Kerala School of Mathematics

Date and Time : February 05, 2021 at 03:00 p.m.

Venue : Seminar Hall, Kerala School of Mathematics

Abstract: In this talk we will derive a non-cusp form of weight

(

, even) for

in the Kohnen plus space whose Petersson scalar product with a cuspidal Hecke eigenform

is equal to a constant times the

value

We also prove that for such a form

and the associated form

under the

Shimura-Kohnen lift the quantity

is algebraic.

Title: Characterization of linear maps preserving unitary conjugation.

Speaker: Dr. Shankar P.

Affiliation: Indian Statistical Institute, Bangalore

Date and Time: January 22, 2021 at 03:00PM

Venue: Seminar Hall, Kerala School of Mathematics

Title: Sign Changes in restricted coefficients of Hilbert Modular forms

Speaker: Krishnarjun K

Affiliation: Harish Chandra Research Institute, Prayagraj(Allahabad)

Date and Time: January 08, 2021 at 03:00PM

Venue: Seminar Hall, Kerala School of Mathematics

Abstract: Let

be an adelic Hilbert cusp form of weight

and level

over a totally real number field

. In this talk, we study the sign changes in the Fourier coefficients of

when restricted to square-free integral ideals and integral ideals in an “arithmetic progression”. In both cases we obtain qualitative results and in the former case we obtain quantitative results as well. Our results are general in the sense that we do not impose any restriction of the number field

, the weight

or the level

.

Title : Some notions of non-commutative convexity

Speaker: Syamkrishnan M. S.

Affiliation: Kerala School of Mathematics

Date and Time: December 04, 2020 at 03:00PM

Venue: Seminar Hall, Kerala School of Mathematics

Abstract: In this talk, we shall introduce two non-commutative versions of the classical convexity, namely the

-convexity and matricial convexity in the setting of

-algebras. We shall discuss the similarities as well as dissimilarities between the convex sets in the classical setting with the convex sets in the non commutative case. Also, we will be discussing its connections with other areas of operator algebras.

Title: On non-vanishing of modular L functions inside the critical strip

Speaker : Sandeep E. M.

Affiliation : Kerala School of Mathematics

Date and Time : November 20, 2020 at 03:00 p.m.

Venue : Seminar Hall, Kerala School of Mathematics

Title : Elliptic Curves: Introduction and An Application

Speaker: Kalyan Chakraborty

Affiliation: Kerala School of Mathematics

Date and Time: November 06, 2020 at 03:00 p.m.

Venue: Seminar Hall, Kerala School of Mathematics

Abstract: This talk will begin with an introduction to elliptic curves. We shall then progress into the BSD conjecture and finally look into the idea of the proof of Fermat’s last theorem.

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.