Presented by: 
Anton Thalmaier (University of Luxembourg)
Mon 28 Jul, 2:00 pm - 2:45 pm
Hawken Building (50), room N202

We describe a construction of Brownian measures on Jordan curves with respect to the Weil-Petersson metric. The step from Brownian motion on the diffeomorphism group of the circle to Brownian motion on Jordan curves in the complex plane requires probabilistic arguments well beyond the classical theory of conformal welding. This difficulty is due to the lack of quasi-symmetry of canonical Brownian motion on Diff(S^1).

The key step in our construction is the systematic use of a Kählerian diffusion on the space of Jordan curves for which the welding functional gives rise to conformal martingales.