- Ruixiang Zhang, IAS
- Kakeya type problems and analysis
- 09/29/2020
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
Informally, Kakeya type problems ask whether tubes with different positions and directions can overlap a lot. One usually expects the answer to be no in an appropriate sense. Thanks to the uncertainty principle, such a quantified non-overlapping theorem would often see powerful applications in analysis problems that have Fourier aspects. Perhaps the most well-known Kakeya type problem is the Kakeya conjecture. It remains widely open in $\Bbb{R}^n (n>2)$ as of today. Nevertheless, in the recent few decades people have been able to prove new Kakeya type theorems that led to improvements or complete solutions to analysis problems that appeared out of reach before. I will give an introduction to Kakeya type problems/theorems and analysis problems that see their applications. Potentially reporting some recent progress joint with Du, Guo, Guth, Hickman, Iosevich, Ou, Rogers, Wang and Wilson.
