Zu Chongzhi Research Seminar

Date and Time (China standard time): Monday, June 29, 4:00 PM – 5:00 PM

Location: WDR 1007

Zoom: 917 9652 1608, Passcode: dkumath

Title: Restriction estimates for toral eigenfunctions and lattice points in spherical regions

Speaker: Cheng Zhang, Tsinghua University

Abstract: We establish new L2 restriction estimates for toral eigenfunctions. These estimates are sharp in certain cases, and thus prove a conjecture of Huang-Zhang for smooth submanifolds of large codimension. In particular, they provide new progress toward a conjecture of Bourgain-Rudnick. The proof combines a slicing and packing method with the approximation of the discrete spherical multiplier by Magyar-SteinWainger and Magyar.

Bio: Cheng Zhang is an Assistant Professor at the Yau Mathematical Sciences Center, Tsinghua University. His research focuses on harmonic analysis. He received his bachelor’s degree from Zhejiang University and his Ph.D. from Johns Hopkins University. He is the principal investigator of the National Overseas High-Level Young Talent Program, an NSFC General Program grant, and a Young Scientist Project under the National Key R&D Program of China.