Off-Diagonal Spectral Cluster Asymptotics on Zoll Manifolds

Explore off-diagonal spectral cluster asymptotics on Zoll manifolds in this 56-minute seminar talk by Blake Keeler from Dalhousie University. Delve into the asymptotic properties of spectral cluster kernels on smooth, compact Riemannian manifolds without boundary. Examine the Schwartz kernel of the orthogonal projection operator and its conjectured universal asymptotic behavior. Learn about the implications for statistical properties of monochromatic random waves and the known cases where the conjecture holds. Discover how Zoll manifolds, where all geodesics are periodic with the same period, demonstrate universal asymptotic behavior for appropriate cluster intervals. Gain insights into this research, which is based on joint work with Yaiza Canzani and Jeffrey Galkowski, presented as part of the Seminar Spectral Geometry in the clouds series at the Centre de recherches mathématiques.