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Stochastic differential equations for Lie group valued moment maps

Date: Friday, November 22, 2019 14:00 - 15:00
Speaker: Daria Smirnova (University of Geneva)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series: Physical Sciences Seminar
Host: Mikhail Lemeshko
Contact: PETZ Caroline

Abstract:

The classical work of Pitman in probability theory establishes a surprizing link between the Brownian motion in dimensions one and three. This relation was interpreted by Biane-Bougerol-O'Connell in terms of the Duistermaat-Heckman measure from symplectic geometry.

We generalize these constructions for the case of Brownian motion on curved three dimensional spaces: the 3-sphere and the hyperbolic space. The case of the hyperbolic space is intimately related to the quantum group U_q(sl(2)). We method is a combination of analytic results and numerical experiements which allowed to rule out some of the scenarios.
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