Georgia Institute of Technology College of Sciences

We consider a diffusion on a potential landscape which is given by a smooth Hamiltonian in the regime of small noise. We give a new proof of the Eyring-Kramers formula for the spectral gap of the associated generator of the diffusion. The proof is based on a refinement of the two-scale approach introduced by Grunewald, Otto, Villani, and Westdickenberg and of the mean-difference estimate introduced by Chafai and Malrieu. The Eyring-Kramers formula follows as a simple corollary from two main ingredients : The first one shows that the Gibbs measure restricted to a domain of attraction has a "good" Poincaré constant mimicking the fast convergence of the diffusion to metastable states. The second ingredient is the estimation of the mean-difference by a new weighted transportation distance. It contains the main contribution of the spectral gap, resulting from exponential long waiting times of jumps between metastable states of the diffusion. This new approach also allows to derive sharp estimates on the log-Sobolev constant. This is joint work with Andre Schlichting.

The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: The University of Alabama at Birmingham, The Georgia Institute of Technology, Emory University, The University of Tennessee Knoxville. The following six speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology: Robert Finn (Stanford University), Bo Guan (Ohio State University), John Harvey (University of Notre Dame), Fernando Schwartz (University of Tennessee), Henry Wente (Toledo, Ohio), Xiangwen Zhang (Columbia University) .

Emory University, Georgia Tech and Georgia State University, with support from the National Science Foundation and the National Security Agency, will continue the series of mini-conferences and host a series of 9 new mini-conferences from 2013-2016. The 11th of these mini-conferences will be held at Georgia State University from January 25-26, 2014. The conferences will stress a variety of areas and feature one prominent researcher giving 2 fifty minute lectures and 4 outstanding researchers each giving one fifty minute lecture. There will also be several 25 minute lecturers by younger researchers or graduate students. For more details, see the schedule

The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: Emory University; Georgia Institute of Technology; University of Alabama at Birmingham; University of Tennessee Knoxville. The following five speakers will give presentations: Alex Freire (University of Tennessee, Knoxville); Matthew Gursky (University of Notre Dame); William Minicozzi II (MIT); Yanir Rubinstein (University of Maryland); Gaoyong Zhang (NYU-Poly). Please email oliker@mathcs.emory.edu if you plan to attend and wish to request support.