Speaker:Prof. Juan J. Manfredi, University of Pittsburgh

Title: Analysis and nonlinear PDE in the Heisenberg Group

Abstract: The Heisenberg group H has a rich history originating in quantum mechanics. It is the simplest non-commutative nilpotent Lie group. It provides the analytic and geometric structure to study degenerate partial differential equations.

This lecture begins with an introduction to the Heisenberg group, starting with the basic definitions and theorems. We then move to partial differential equations. Topics include: the horizontal Laplacian, horizontal Mean Value Gauss-Koebe formula, Brownian motion Viscosity solutions the p-Laplacian, and Tug of War.