Title: Stochastic Target Approach to Ricci Flow on Surfaces
Speaker: Ionel Popescu
Speaker Info: Georgia Tech and Romanian Academy
Special Note: Note the special time of the seminar for this talk.
We first set up a stochastic target approach to the Ricci flow in surfaces. Using this though we prove that the normalized Ricci flow converges to a constant curvature metric on all surfaces of non-positive Euler characteristic. This convergence takes place in all $C^k$ topology and happens exponentially fast. The main technique we use is couplings of time changes Brownian motions. This gives the $C^0$ and $C^1$ convergence. However to get the $C^2$ convergence we introduce a novel technique which is a coupling of three particles.Date: Monday, December 10, 2012
Our approach gives sort of ergodic like picture of why the normalized Ricci convergence takes place. This ergodicity is probabilistically viewed via coupling alluded above. This is joint work with Robert W. Neel.