Graduate Student Colloquium
Alex Austin
UIC
The Quasiconformal Jacobian Problem
Abstract: If two metric spaces are bi-Lipschitz equivalent, then they are effectively the same. Using the fundamental question, 'When is a metric space bi-Lipschitz equivalent to the Euclidean space $\mathbb{R}^n$?', as motivation, I will introduce the (still far from solved) quasiconformal Jacobian problem: characterize those weights on $\mathbb{R}^n$ comparable to the Jacobian of a quasiconformal map.
I will discuss a result of Bonk, Heinonen and Saksman which displays a class of weights which are comparable to quasiconformal Jacobians, and a result of Kovalev and Maldonado which gives information on how wide to cast your net if you seek a characterization.
Pizza will be served.
Thursday February 13, 2014 at 4:00 PM in SEO 636