Annual Progress seminar

Tuesday,14 March 2023, 11.30 am

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Venue: Room 105

Host: Shripad M. Garge

Speaker: Deepkumar Makadiya

Affiliation: IIT Bombay

Title: Twisted Chevalley groups

Abstract: The talk aims at discussing the twisted Chevalley group and its automorphisms. The first part of the talk deals with the existing literature regarding the twisted Chevalley group and we present some results in this direction. The main aim of the second half is to characterize the class of automorphisms of the twisted Chevalley group. En route, we present some useful results to build the setting of the desired characterization.

Number Theory seminar

Tuesday, 14 March 2023, 2.30 pm

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Venue: Google meet: Link: https://meet.google.com/jtv-udzf-bbx

Host: Kummari Mallesham

Speaker: Keshav Aggarwal

Affliation: Alfréd Rényi Institute of Mathematics

Title:  Analytic study of L-functions: Subconvexity bound problem

Abstract: Much of modern number theory revolves around the study of L-functions. The L-functions associated with arithmetic objects called automorphic forms are of great interest and many conjectures have been made about their properties. The best known is the Riemann hypothesis (RH) which has many well-known consequences. One such is the Lindelof hypothesis (LH) which is a conjecture about the growth rate of automorphic L-functions on the critical line. Results achieving partial progress towards LH are known as Subconvexity Bound results and have rich arithmetic applications, like equidistribution of points on certain surfaces, and Quantum Unique Ergodicity. Recent years have seen much activity in this area by combining powerful tools like the Delta method, Motohashi-type formulas, and estimates on moments of L-functions. In this talk, we give an introduction to the subconvexity bound problem and a recent result on bounding a short second moment of GL(3) L-functions. This is joint work with Joseph Leung and Ritabrata Munshi and yields the yet best-known subconvexity bound for GL(3) L-functions in the t-aspect.

Algebraic Groups Seminar

Tuesday, 14 march 2023, 4 pm

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Venue: Room 114

Host: Shripad M. Garge

Speaker: Deepkumar Makadiya

Affiliation: IIT Bombay

Title: Linear algebraic groups, basic themes. IV

Abstract: We complete the discussion around the Jordan decomposition in this lecture.