报告题目：Sharp Spectral-Cluster Restriction Bounds for Orthonormal Systems

报告人：王兴副教授，湖南大学

报告时间：2025年6月13日（周五）9:00

报告地点：20-306

报告摘要：For a smooth k-dimensional submanifold Σ of a d-dimensional compact Riemannian manifold (M,g), we extend the L^p(Σ) restriction bounds of Burq, Gérard, and Tzvetkov [Duke, 2007] from individual Laplace–Beltrami eigenfunctions to systems of L^2(M)-orthonormal functions. Our bounds are essentially optimal for every triple (k,d,p) with p ≥ 2, except possibly when d ≥ 3, k = d−1, and 2 ≤ p < 4. This work is inspired by Frank and Sabin [Adv. Math, 2017], who established analogous L^p(M) bounds for L^2(M)-orthonormal systems.

报告人简介：王兴，湖南大学数学学院副教授。美国约翰霍普金斯大学博士学位，师从Christopher Sogge教授。主要研究方向是流形上的调和分析及算子谱的渐近性质，在Advances in Mathematics, Transactions of American Mathematical Society, Canadian Journal of Mathematics等学术知名期刊上发表多篇学术论文。

邀请人：现代分析及其应用数学研究所