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Discrete Analysis Seminar

Tuesday, January 25, 2022
3:00pm to 4:00pm
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Harmonic analysis over $\mathbb{Q}_p$ and decoupling
Zane Li, Department of Mathematics, Indiana University Bloomington,

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 $\lesssim_{\varepsilon} (\log N)^{2 + \varepsilon}$. No familiarity of the $p$-adic analysis will be assumed.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].