Semiclassical analysis, geometric representation and quantum ergodicity

Time:Fri.,10:00-11:00am, Mar. 31, 2023

Venue:Zoom ID: 618-038-6257, PW: SCMS

Organizer:Chen Xi(Fudan), Long Jin(Tsinghua)

Speaker:Minghui Ma (Chinese Academy of Sciences)


Quantum Ergodicity (QE) is a classical topic in spectral geometry, which 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 the QE for unitary flat bundles. By using a mixture of semiclassical and geometric quantizations, we can deal with the high frequency eigensections of a series of unitary flat bundles simultaneously. We will also give some applications on flat sphere bundles over hyperbolic surfaces.

DATEMarch 31, 2023
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