**DIFFERENTIAL
GEOMETRY SEMINAR**

**"**Extremal Kähler Metrics and
Bach-Maxwell Equations**"**

By

# CANER KOCA

# (VANDERBILT UNIVERSITY)

** **

**Abstract: **Extremal Kähler metrics are introduced by Calabi
in 1982 as part of the quest for finding "canonical" Riemannian
metrics on compact complex manifolds. Examples of such metrics include the Kähler-Einstein metrics, or more generally, Kähler metrics with constant scalar curvature. In this
talk, I will start with an expository discussion on extremal
metrics. Then I will show that, in dimension 4, these metrics satisfy a conformally-invariant version of the classical
Einstein-Maxwell equations, known as the Bach-Maxwell equations, and thereby
are related to physics (conformal gravity) in a surprising and mysterious way.

**Date: ****Tuesday, June
3, 2014**

**Time: ****15:40 **

**Place: ****Mathematics Seminar Room,
SA-141**

** **

** **

**All are most cordially invited.**

Tea and biscuits: after the seminar