Speaker: Prof. Danqing He (Fudan University)

Title: Some new local smoothing estimates

Time: 10:00-11:00 August 16, 2026 (Sunday)

Inviter: Prof. Qingtang Su (MCM, CAS)

Place: MCM110

Abstract: The local smoothing conjecture for wave equations is an important longstanding problem in modern harmonic analysis, closely connected with Fourier restriction theory. We improve the previously best-known local smoothing estimates both on compact Riemannian manifolds and in Euclidean space. In particular, on general compact Riemannian manifolds, we obtain the conjectured sharp estimates in all odd dimensions, which are optimal in view of the counterexamples of Minicozzi and Sogge.

This is joint work with Shengwen Gan, Xiaochun Li, and Shukun Wu.