TItle: Harmonic analysis over $\mathbb{Q}_p$ and decoupling

Speaker: Zane Li, Indiana University Bloomington

Abstract: In this talk, we discuss harmonic analysis over the $\mathbb{Q}_p$. Compared to when working over $\mathbb{R}$, tools such as the uncertainty principle and wavepacket decomposition are not just useful heuristics, but rigorously true. Additionally, decoupling estimates over $\mathbb{Q}_p$ are still strong enough to imply exponential sum applications which have been key applications of real decoupling theorems. This observation along with an optimization of the Guth-Maldague-Wang argument allowed the speaker with Shaoming Guo and Po-Lam Yung to show that the discrete restriction constant for the parabola is $\lesssim_{\varepsilon} (\log N)^{2 + \varepsilon}$.

About the speaker: Zane Li received his PhD from UCLA under the supervision of Fields medalist Terence Tao. His research area is harmonic analysis and interactions with number theory. He currently works at Indiana University Bloomington with Ciprian Demeter. He published high quality papers at top journals: Transactions of the American Mathematical Society, American Journal of Mathematics, Revista Matematica Iberoamericana, Mathematics of Computation, etc.

时间：2021年11月25日（周四）10:00-11:00

地点：腾讯会议 ID: 461 054 306

邀请人：孟宪昌