Title: Circle Method and Automorphic Forms
Speaker: Wenzhi Luo
Abstract: In this lecture, we will present an introduction to a well-known method in Analytic Number Theory, the Circle Method. It was first introduced by Hardy and Littlewood in 1920s in a series of papers entitled Some problems of ‘Partitio Numerorum’ on the classic Waring’s problem, and further refined by Kloosterman in 1925. We’ll focus on some of its recent developments, most notably the proof of Vinogradov mean-value conjecture by Bourgain-Demeter-Guth via the l2 decoupling technique in harmonic analysis, and striking applications to the analytic theory of automorphic forms.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for two credit hours of Math 6193 with Professor Nimish Shah.
