Isoperimetric and Functional Inequalities on Discrete Spaces

Research Horizons Seminar
Wednesday, February 22, 2012 - 12:05
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
Following exciting developments in the continuous setting of manifolds (and other geodesic spaces), in joint works with various collaborators, I have explored discrete analogs of the interconnection between several functional and isoperimetric inequalities in discrete spaces. Such inequalities include concentration, transportation, modified versions of the logarithmic Sobolev inequality, and (most recently) displacement convexity. I will attempt to motivate and review some of these connections and illustrate with examples. Time permitting, computational aspects of the underlying functional constants and other open problems will also be mentioned.