Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case

Symplectic Dynamics/Geometry Seminar
Topic:Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case
Speaker:Nikhil Savale
Affiliation:University of Cologne
Date:Monday, October 28
Time/Room:3:30pm - 4:30pm/Simonyi Hall 101
Video Link:https://video.ias.edu/sympdyngeo/2019/1028-NikhilSavale

We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional quasi-contact case. A key role in all results is played by the presence of abnormal geodesics and represents the first such appearance of these in sub-Riemannian spectral geometry.