Stochastic Target Approach to Ricci Flow on surfaces

Series: 
Stochastics Seminar
Thursday, September 27, 2012 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
School of Mathematics, Georgia Tech
 Ricci flow is  a sort of (nonlinear) heat problem under which the metric on a given manifold is evolving.  There is a deep connection between probability and heat equation.  We try to setup a probabilistic approach in the framework of a stochastic target problem. A major result in the Ricci flow is that the normalized flow (the one in which the area is preserved) exists for all positive times and it converges to a metric of constant curvature.  We reprove this convergence result in the case of surfaces of non-positive Euler characteristic using coupling ideas from probability.   At certain point we need to estimate the second derivative of the Ricci flow and for that we introduce a coupling of three particles.     This is joint work with Rob Neel.