Introduction to Bergman geometry

Series
Geometry Topology Seminar
Time
Wednesday, October 2, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jihun Yum – Gyeongsang National University in South Korea
Organizer
John Etnyre

The Poincaré metric on the unit disc $\mathbb{D} \subset \mathbb{C}$, known for its invariance under all biholomorphisms (bijective holomorphic maps) of $\mathbb{D}$, is one of the most fundamental Riemannian metrics in differential geometry.

In this presentation, we will first introduce the Bergman metric on a bounded domain in $\mathbb{C}^n$, which can be viewed as a generalization of the Poincaré metric. We will then explore some key theorems that illustrate how the curvature of the Bergman metric characterizes bounded domains in $\mathbb{C}^n$ and more generally, complex manifolds. Finally, I will discuss my recent work related to these concepts.