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.)