Noncommutative Geometry Seminar

Date: April 18, 2024

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Qiaochu Ma, Washington University in St. Louis

Title: Mixed quantization and quantum ergodicity

Abstract: Quantum Ergodicity (QE) is a classical topic in spectral geometry and quantum chaos, it states that on a compact Riemannian manifold whose geodesic flow is ergodic with respect to the Liouville measure, the Laplacian has a density-one subsequence of eigenfunctions that tends to be equidistributed. In this talk, we present a uniform version of QE for a certain series of unitary flat bundles using a mixture of semiclassical and geometric quantizations. We shall see that even if analytically unitary flat bundles are similar to the trivial bundle, the holonomy provides extra fascinating geometrical phenomena.