Analysis Seminar

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When the Schrödinger equation meets number theory

Speaker: Ciprian Demeter, Indiana University

Location: Warren Weaver Hall 1302

Date: Thursday, April 25, 2024, 11 a.m.

Synopsis:

The question of pointwise convergence of the solution of the free Schrödinger equation to the initial data has motivated significant developments in harmonic analysis. Incidence geometry, refined Strichartz estimates and decoupling are some of the tools that proved instrumental for Euclidean spatial domains. These tools seem to be ineffective in the case of tori, and the problem is open even in one spatial dimension. I will describe progress on this case that involves completely different tools, a mix of number theory and combinatorics.