## Analysis Learning Seminar

# Sobolev extension of Lipschitz mappings into metric spaces

## Scott Zimmerman (University of Connecticut)

### Friday, September 15, 2017
3:30 pm

MONT 314

The Heisenberg group was first described by Herman Weyl, and it is named after Werner Heisenberg (as he was the first to study the Lie algebra associated with the group). Since it's origin, the Heisenberg group has been an object of study in many fields in analysis, geometry, and physics. In this talk, I will introduce the group and provide some of its interesting analytic and geometric properties. As a point of illustration, I will discuss the structure of geodesic curves in the group. In the case n=1, this is simple. However, deducing the structure of these curves in higher dimensions requires proof, and I will present such a proof from a paper by Piotr Hajlasz and me.