### The Geometry of Logconcave Functions

- Series
- ACO Student Seminar
- Time
- Wednesday, February 25, 2009 - 13:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Daniel Dadush – ISyE, Georgia Tech

In this talk, I will introduce the class of logconcave and s-concave functions, illustrate their properties, and explain their connections to convex geometry. I will present a simple and unified approach for proving probabilistic inequalities for logconcave and s-concave densities on the real line. Lastly I will use these techniques to prove two important theorems in convex geometry: Grunbaum's theorem, every halfspace cut through the centroid of a convex body contains at least a 1/e volume fraction of the body, and the Milman-Pajor inequality, a convex body in R^n is sandwiched between its inertial ellipsoid and a factor n scaling of it. Joint work with Santosh Vempala.