PROGRAM
ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID)

ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS)
DATE: 08 August 2022 to 19 August 2022
VENUE: Ramanujan Lecture Hall and online

The program plans to focus on recent developments in the arithmetic of Elliptic curves and special values of L-functions.

ICTS is committed to building an environment that is inclusive, non-discriminatory and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.

CONTACT US: ecl@icts.res.in
PROGRAM LINK: https://www.icts.res.in/program/ecl2022

Table of Contents (powered by https://videoken.com)
0:00:00 Bounds for L-functions
0:00:52 Introduction
0:05:07 Critical strip
0:07:13 Subconvexity problem
0:09:59 (Hardy-Littlewood-) Weyl bound
0:11:02 Proof of Weyl bound
0:15:15 An application
0:21:10 Another family of L-values
0:23:51 Lattice points on sphere
0:28:09 Lattice points on sphere and subconvexity
0:31:38 Automorphic L-functions
0:33:40 Main Conjectures
0:35:53 The Subconvexity Problem
0:37:53 Spectral aspect subconvexity and quantum chaos
0:41:24 Subconvex bounds - 1
0:44:49 Subconvex bounds - 2
0:50:24 Classical Methods
0:52:24 Modern Methods
0:54:14 Burgess bound via delta method
0:57:01 Open problems
0:59:08 Q&A