Thematic Seminar: The ubiquity of Fourier restriction

Seminar | January 28 | 4:10-5 p.m. | 740 Evans Hall

 Ruixiang Zhang, University of Wisconsin-Madison

 Department of Mathematics

In Fourier analysis, there is a class of questions known as Fourier restriction type problems. A lot of people have tried to answer this kind of questions, partly because they naturally show up in the study of many problems in PDE, spectral theory, number theory, geometric measure theory and combinatorics. I will talk about three examples of Fourier restriction type problems I recently worked on (based on joint results with Du, Guo, Guth and Wang), highlighting their connections to neighboring subjects. Then I will describe what a general Fourier restriction type problem is like. Time permitted I will also talk about a few useful things one can do to study those problems.