Anton Alekseev (Geneva)

Momentum maps and stochastic processes


There is an intimate relation between the theory of momentum maps in symplectic geometry and the theory of stochastic processes. Bian, Bougerol and O'Connell (BBC) showed that Duistermaat-Heckman measures from the momentum map theory have a natural interpretation as conditional probabilities for solutions of certain stochastic differential equations.

 The momentum map theory admits several versions. Besides the one mentioned above, there are so-called theories of Lie group valued momentum maps. In the talk, we will explain how to adapt the BBC formalism to this case. Our main example will be the space of 2 by 2 matrices (with various extra conditions). No previous knowledge of symplectic geometry is required.

 The talk is based on a joint work in progress with E. Arzhakova and D. Smirnova.