Speaker: Professor Yueh-Ju Lin (Wichita State Universit)

Title:  Local and global conformal invariants and Gauss-Bonnet type formulas

Abstract:  Conformal invariants are fundamental tools for understanding the geometry of manifolds and for solving geometric problems. In this talk, I will first introduce Q-curvature, the Gauss-Bonnet-Chern formula, and their connections to higher-order geometric PDEs on compact manifolds. I will then turn to global invariants, focusing on the renormalized volume of Poincare - Einstein (PE) manifolds. Examples of PE manifolds include the hyperbolic ball model. These are complete Einstein manifolds with a well-defined conformal boundary. Understanding such global invariants is a key step in studying the moduli space of PE manifolds. I will discuss a Gauss-Bonnet-type formula that relates the renormalized volume to the integral of a scalar conformal invariant and, time permitting, a new approach for computing global integral invariants of PE manifolds. This is a joint work with Jeffrey Case, Ayush Khaitan, Aaron Tyrrell, and Wei Yuan.