Rice University Department of Mathematics Colloquium

Kostant-Ngô Integration of Hamiltonian Systems

4:00 pm Thursday, October 5, 2017
David Ben-Zvi (UT Austin)

Abstract: Lie groups provide a fertile source of Hamiltonian systems, both classical and quantum. The classical systems come via moment maps from the invariant polynomials of a Lie algebra, while the quantum systems come from the Harish-Chandra center of the enveloping algebra - for example, acting as commuting differential operators on locally symmetric spaces. I will explain how ideas of Kostant and Ngô (from the proof of the Fundamental Lemma) allow one to integrate the flows of all the resulting classical Hamiltonian systems. I will then show how this construction may be quantized, resulting in a new integration of quantum Hamiltonian systems. Time permitting I'll discuss our motivation, an application to the topology of character varieties of surfaces. (Based on joint work with Sam Gunningham.)

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