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
Place: Mathematics Seminar Room, SA-141
All are most cordially invited.
Tea and biscuits: after the seminar