Periodic Reporting for period 4 - SymplecticEinstein (The symplectic geometry of anti-self-dual Einstein metrics)
Periodo di rendicontazione: 2020-03-01 al 2021-08-31
Solutions to Einstein's field equations are possible models for the universe. Finding solutions is as difficult as it is important. The aim of this project is to exploit the hidden symplectic geometry of these equations which I recently discovered together with co-authors. This confluence of two different geometries makes many new potential techniques available to either side. The overall objective is to both find new solutions to Einstein's equations and better understand the solutions we already have. Moreover, I will use techniques from the study of Einstein metrics to explore the symplectic manifolds which arise this way.
Our results have been diseminated by publication in scienfitc journals, as is usual for pure mathematics. I have also recorded a short video (in French) explaining some of the ideas behind the project to a general audience. You can watch this on Facebook, or on the webpage of the Fondation ULB: https://fondationulb.be/fr/geometrie.