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Brownian motion on Riemannian Manifolds and Riemann surfaces

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  • UserMatthis Lehmkuehler
  • ClockThursday 15 March 2018, 13:00-14:00
  • HouseMR13.

If you have a question about this talk, please contact Loren E. Held.

Brownian motion in two dimensions is conformally invariant which allows us to define Brownian motion (up to time reparametrisation) on Riemann surfaces without having to pick a metric. After discussing this construction in some detail, I will talk about the relationship of this object to Brownian motion on Riemannian manifolds and we will then have a closer look at properties of Brownian motion and Brownian bridges on Riemann surfaces. Covering space theory and the uniformisation theorem for Riemann surfaces will allow as to study global properties (like the homotopy class) of these random paths.

This talk is part of the Part III Seminars series.

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