# Geometry of canonical metrics on Kähler manifolds

- Date
- May 14 at 16:00 - 18:10, 2021 (JST)

- Speaker
- Dr. Eiji Inoue (Special Postdoctoral Researcher, iTHEMS) Edit

- Venue
- via Zoom

- Language
- English

The aim of this talk is to report recent trends in Kähler geometry. Kähler geometry consists of two aspects: the one is algebraic geometry and the other is metric geometry.The first one hour is an introduction for non-mathematicians.

I begin with a simple example of algebraic variety from ancient Greek, which I believe is the simplest example illustrating motivation for compact complex manifolds.

On the other hand, I explain the first motivation for canonical metrics in Kähler geometry via Riemann’s uniformization theorem.The last one hour is an introduction to recent trends in Kähler geometry, especially Kähler-Einstein metrics.

The existence of Kähler-Einstein metrics turns out to be related to geometry of degenerations of space, which is so called Yau-Tian-Donaldson conjecture.

I explain various aspects of this topic. We encounter deep studies in metric geometry, birational geometry and non-archimedean geometry.

I finally explain recent breakthrough on Kähler-Ricci flow.The goal of this talk is the starting point of my study. I briefly explain my study if time permits.

*Please contact Keita Mikami's mail address to get access to the Zoom meeting room.