# MRC Week 1b, June 3 – 9, 2018

## Harmonic Analysis: New Developments on Oscillatory Integrals

Organizers:
Philip T. Gressman, University of Pennsylvania
Larry Guth, Massachusetts Institute of Technology
Lillian B. Pierce, Duke University

This workshop will focus on two closely related topics within harmonic analysis that have undergone important new developments. First, we will study the solution of the $l^2$-decoupling conjecture by Bourgain and Demeter, and further work with Guth, which resolved a seventy-year-old problem in analytic number theory, the Main Conjecture in the Vinogradov Mean Value Method. This has close ties both to the Hardy-Littlewood circle method and to aspects of the Riemann zeta function. Second, we will explore ideas from a broad program in multilinear oscillatory and singular integrals that has been initiated by Christ, Li, Tao, and Thiele.

These two areas have the potential for close interactions, due to the critical role that multilinear perspectives play in the work on decoupling. The substantial recent developments within both areas have involved the development of new tools which may apply to a range of other arithmetic and analytic problems, and these areas hold many opportunities for valuable contributions by early-career mathematicians.

The application period is closed. No further applications will be accepted.