Gunhee Cho

University of Connecticut

Talk Title: Invariant metrics in complex geometry 

Abstract: This talk is a gentle introduction to complex geometry for a general audience that has taken at least one course in complex analysis. Crucial theorems in complex analysis like Schwarz lemma, Riemann mapping theorem, and Uniformization theorem lead us to the natural question: How can we understand complex manifolds based on the observation of the Poincare-disk in the complex Euclidean plane? We will introduce the intrinsic metrics; Caratheodory, Kobayashi, Bergman, and the Kahler-Einstein metrics, and we will see how these metrics help us to understand a large class of complex manifolds. If time allows, I will introduce my papers related to the talk: https://arxiv.org/abs/1806.06311, https://arxiv.org/abs/1812.05398