Fourier restriction type problems: New developments in the last 15 years

Speaker 

Ruixiang Zhang is an assistant professor in the Department of Mathematics. He works in harmonic analysis on Euclidean spaces and related problems. He is also interested in harmonic analysis on general locally symmetric spaces and in additive combinatorics.

Awards for Zhang include the Gold Medal of the 49th International Mathematics Olympiad, a Silver Medal for his doctoral thesis for the New World Mathematics Awards, and the Frontier of Science Award. He currently holds a Sloan Research Fellowship (2022-24). In 2023, he was awarded the SASTRA Ramanujan Prize for his outstanding contributions in mathematics.

Abstract

Fourier restriction type problems form a class of important problems in harmonic analysis. They are also related to PDE, analytic number theory, geometric measure theory and mathematical physics. In the past 15 years, much progress has been made on these problems. In this talk, we will introduce Fourier restriction type problems and survey some recent results, and then conclude by mentioning some personal favorite future directions.