Graduate Student Colloquium
Alex Austin
UIC
The Heisenberg group and its Horizontal Calculus
Abstract: This is the second of two talks. In the first we saw quasiconformal maps on $\mathbb{R}^n$ generated by vector field flows, and using convex potentials, in order to approach the quasiconformal Jacobian problem. In this talk I will introduce the Heisenberg group, its Lie algebra structure, and explain how the latter gives rise to a horizontal distribution to which we associate a metric. Though this metric renders the space highly non-Euclidean, we can develop a calculus compatible with the horizontal structure and there is a well developed theory of quasiconformal maps. I will explain that the ingredients of the first talk, vector field generators and notions of convexity, are all present, and allow an attempt at the results of the first talk in this new setting.
Pizza will be served after the talk.
Thursday February 20, 2014 at 4:00 PM in SEO 636