Claude LeBrun: Einstein Metrics, Four-Manifolds, and Conformally Kähler Geometry

Date: 2023-07-10

Time: 09:00 - 10:00


Claude LeBrun, Stony Brook University


Peculiar features of 4-dimensional geometry make dimension four into a “Goldilocks zone” for Einstein metrics, with local geometric flexibility of solutions managing to coexist with global strong-rigidity results for Einstein metrics on certain compact 4-manifolds. This talk will survey aspects of the interplay between Einstein metrics and smooth topology on compact symplectic 4-manifolds. We will see how ideas from K ̈ahler and conformal geometry allow us to construct. Einstein metrics on many such manifolds, while a complimentary tool-box shows that these existence results are optimal in certain specific contexts. We will then go on to describe what is currently known concerning the question of whether the metrics constructed by these techniques sweep out the entire moduli space of Einstein metrics on specific compact 4-manifolds.