Zu Chongzhi Research Seminar

Date and Time (China standard time): Sunday, Nov 2, 9:30 am – 10:30 am

Location: WDR 1007

Zoom: 8743103217, Passcode: dkumath

Title: Curved Kakeya problems

Speaker: Yakun Xi, Zhejiang University

Abstract: We study curved Kakeya sets defined by Hormander phase functions. We show that the analysis of curved Kakeya sets arising from translation-invariant phase functions under Bourgain’s condition, as well as Nikodym sets on manifolds with constant sectional curvature, can be reduced to the study of standard Kakeya sets in Euclidean space. Combined with the recent breakthrough of Wang and Zahl, our work establishes the Nikodym conjecture for three-dimensional manifolds with constant sectional curvature. On the other hand, we show that for generic positive definite Hormander phase functions, the associated curved Kakeya sets have Hausdorff dimension strictly greater than (n+1)/2, surpassing the Kakeya compression threshold.

Bio: Yakun Xi is a researcher and tenured associate professor at the School of Mathematical Sciences, Zhejiang University. He studied in the Department of Mathematics at Zhejiang University from 2008 to 2012 and received his bachelor’s degree in Mathematics and Applied Mathematics. From 2012 to 2017, he completed his PhD at Johns Hopkins University in the United States under the supervision of Professor Christopher D. Sogge. From 2017 to 2020, he was a visiting assistant professor at the University of Rochester (USA). He joined the School of Mathematical Sciences at Zhejiang University in August 2020 as a research professor, and has served as a tenured associate professor since 2024.