Student Harmonic Analysis and PDE Seminar (HADES): Algebraic structure underlying Kakeya-type problems

Seminar | October 10 | 3:40-5 p.m. | 891 Evans Hall

 Marina Iliopoulou, UC Berkeley

 Department of Mathematics

Kakeya-type questions ask how much tubes that point to different directions overlap. Such problems are central in harmonic analysis, due to their connection with restriction theory, geometric measure theory, PDE and number theory. Over the years there was some indication that Kakeya-type problems have an underlying algebraic structure, but it was only a decade ago that a tool was introduced in the area to reveal such structure, leading to important advances in the field. This tool is the polynomial method. During this talk we will explain the method and see applications to Kakeya-type problems.