Lossless Strichartz estimates in the prescence of hyperbolic trapping

par Zhongkai Tao (IHES)

lundi 23 févr. 2026, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

The Strichartz estimate is an important estimate in proving the well-posedness of dispersive PDEs. People believed that the lossless Strichartz estimate could not hold on manifolds with trapping (for example, the local smoothing estimate always comes with a logarithmic loss in the presence of trapping). Surprisingly, in 2009, Burq, Guillarmou, and Hassell proved a lossless Strichartz estimate for manifolds with trapping under the “pressure condition”. I will talk about their result as well as our recent work with Xiaoqi Huang, Christopher Sogge, and Zhexing Zhang, which goes beyond the pressure condition using the fractal uncertainty principle and a logarithmic short-time Strichartz estimate. If time permits, I will also talk about the lossless spectral projection estimate in the same setting.