# Phase transitions and conic geometry

Thursday, April 26, 2018 - 3:30pm - 4:30pm

Vincent 16

Joel Tropp (California Institute of Technology)

A phase transition is a sharp change in the behavior of a mathematical model as one of its parameters changes. This talk describes a striking phase transition that takes place in conic geometry. First, we will explain how to assign a notion of dimension to a convex cone. Then we will use this notion of dimension to see that two randomly oriented convex cones share a ray with probability close to zero or close to one. This fact has implications for many questions in signal processing. In particular, it yields a complete solution of the compressed sensing problem about when we can recover a sparse signal from random measurements. This talk is designed for a general mathematical audience.

Based on joint works with Dennis Amelunxen, Martin Lotz, Mike McCoy, and Samet Oymak.

Based on joint works with Dennis Amelunxen, Martin Lotz, Mike McCoy, and Samet Oymak.