The Department of Mathematics is hosting a series of colloquia, open for all to attend. On 9 October 2025, Claude LeBrun from Stony Brook University will give a talk on 'Einstein Constants and Differential Topology'.

Registration:

This talk will take place in person at King's College London in Bush House (SE) 1.01. It will be streamed online via Microsoft Teams. Please click 'Register for this event' to sign up for either an In-Person Ticket or an Online Ticket. If you wish to attend the in-person event, you must select the correct ticket type.

A reception will follow afterwards in Bush House (SE) 1.05.

Abstract

Einstein Constants and Differential Topology

A Riemannian metric is said to be Einstein if it has constant Ricci curvature. In dimensions 2 or 3, this is actually equivalent requiring the metric to have constant sectional curvature. However, in dimensions 4 and higher, the Einstein condition becomes significantly weaker than constant sectional curvature, and this has rather dramatic consequences. In particular, it turns out that there are high-dimensional smooth closed manifolds that admit pairs of Einstein metrics with Ricci curvatures of opposite signs. After explaining how one constructs such examples, I will then discuss some recent results exploring the coexistence of Einstein metrics with zero and positive Ricci curvatures.

About the Speaker: 

Claude LeBrun (Stony Brook University) is a distinguished mathematician working in differential geometry. He earned his doctorate at Oxford under Roger Penrose and has spent most of his career at Stony Brook, while also holding positions at IHÉS, MSRI, and the Institute for Advanced Study. Claude LeBrun is widely known for his influential work on 4-manifolds, complex and conformal geometry, Einstein metrics, and scalar curvature. He was an invited speaker at the 1994 International Congress of Mathematicians and is a Fellow of the American Mathematical Society.

Learn more about Claude LeBrun on the Stony Brook website and also on Wikipedia.

Future colloquia

Please check our event series for details of upcoming speakers.