Analysis Seminar

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Ruling out periodicity in quantum chaos

Speaker: Alex Cohen, NYU

Location: Warren Weaver Hall 1302

Date: Thursday, November 20, 2025, 11 a.m.

Synopsis:

The quantum unique ergodicity conjecture (QUE) predicts that on hyperbolic manifolds, high-frequency Laplace eigenfunctions are always equidistributed. This conjecture fails in a closely related system, quantum cat maps. QUE fails because the cat map analogue of the wave equation is periodic with a small period. In work in progress with Semyon Dyatlov, we develop new harmonic analysis tools to distinguish quantum cat maps from hyperbolic manifolds. In particular, the wave equation on hyperbolic manifolds is not (approximately) periodic with such a small period.