## Voyageur Colloquium: Peter Pivovarov

- Date: 03/15/2013
- Time: 16:00

Lecturer(s):
Peter Pivovarov,

*University of Missouri*
Location:

University of Calgary

Topic:

Gaussian random sets: on the interplay between probability and convexity

Description:

Given a sample of random vectors drawn from the standard Gaussian distribution, there is a variety of associated random convex sets. For instance, taking the convex hull of the vectors gives rise to a Gaussian random polytope. Recently, techniques have been developed to understand the distribution of the volume of such sets, leading to deep results such as central limit theorems and laws of large numbers.

I will discuss a general framework for random convex sets generated by Gaussian matrices. This entails many common models such as convex hulls and Minkowski sums. The focus of the talk will be on connections between stochastic geometry and concentration of measure. In particular, how the probabilistic behavior of volume conveys geometric information about convex sets (based on joint work with Grigoris Paouris).

Bio: Peter was an undergraduate at the University of Calgary until 2003 when he moved to pursue his PhD with Nicole Tomczak-Jaegermann in Edmonton with an NSERC, Ralph Steinhauer and an Izaak Walton Killam Graduate Scholarship, and further earning theJosephine M. Mitchell Research Prize. During that period, he also held various fellowships at the University of Athens, the Institute of Mathematics of the Polish Academy of Sciences, and the Institut Henri Poincaré. This was followed by a Postdoctoral Fellowship at the Fields Institute and a visiting position at Texas A&M University before joining the University of Missouri-Columbia in 2012.

Given a sample of random vectors drawn from the standard Gaussian distribution, there is a variety of associated random convex sets. For instance, taking the convex hull of the vectors gives rise to a Gaussian random polytope. Recently, techniques have been developed to understand the distribution of the volume of such sets, leading to deep results such as central limit theorems and laws of large numbers.

I will discuss a general framework for random convex sets generated by Gaussian matrices. This entails many common models such as convex hulls and Minkowski sums. The focus of the talk will be on connections between stochastic geometry and concentration of measure. In particular, how the probabilistic behavior of volume conveys geometric information about convex sets (based on joint work with Grigoris Paouris).

Bio: Peter was an undergraduate at the University of Calgary until 2003 when he moved to pursue his PhD with Nicole Tomczak-Jaegermann in Edmonton with an NSERC, Ralph Steinhauer and an Izaak Walton Killam Graduate Scholarship, and further earning theJosephine M. Mitchell Research Prize. During that period, he also held various fellowships at the University of Athens, the Institute of Mathematics of the Polish Academy of Sciences, and the Institut Henri Poincaré. This was followed by a Postdoctoral Fellowship at the Fields Institute and a visiting position at Texas A&M University before joining the University of Missouri-Columbia in 2012.

Other Information:

Location: MS 431