Today's seminar will feature a talk by Robert Neel from Lehigh University.
Rob will speak about martingales associated to geometric structures (full
title and abstract below). See you this afternoon!
Seminar Time & Location: 3:30pm in MSB 109A
Title: Degenerate martingales arising from various geometric stuctures,
including minimal surfaces
Abstract:
We first discuss a class of degenerate martingales (which we will call
rank-n martingales) that arises naturally as the diffusion associated with
minimal submanifolds, mean curvature flow, and some sub-Riemannian
structures. This provides a unified approach to "coarse" properties, such
as transience, of such structures. We then specialize to minimal surfaces
in R^3, in which case the associated rank-2 martingale (which is just
Brownian motion on the surface, viewed as a process in R^3) has the
additional property that the tangent plane also evolves as a martingale.
Taking advantage of this extra structure, we develop an extrinsic analogue
of the mirror coupling of two Brownian motions. This allows us to study
finer geometric and analytic properties of minimal surfaces, such as
intersection results (strong halfspace-type theorems) and Liouville
properties.
*Current & Upcoming Seminar Talks*
* April 10 - Robert Neel (Lehigh University)*
April 17 - Tess Anderson (Brown University)
April 24 - Alexander Roitershtein (Iowa State University)
May 1 - Samuel Watson (MIT)
--
*Dr. Matthew Badger*, Assistant Professor
Department of Mathematics, University of Connecticut
www.math.uconn.edu/~badger/
