Colloquium Math : Joel Fine (ULB) : The geometry of Einstein's equations

Thursday 8 Dec 2016, 16:00 → 18:00 Europe/Brussels

CYCL01 (Marc de Hemptinne)

Résumé: Einstein’s equations play a central role in physics, but I will try to explain how they are also of fundamental importance in geometry. In the first part of the talk I will describe the equations themselves, how to solve them in 2D and, briefly, how they have led to huge advances in our understanding of geometry in two and three dimensions. In the second part of the talk, I will discuss the Yamabe programme, which attempts to find Einstein metrics via the calculus of variations, and explain why it remains unsuccessful despite great efforts since it’s introduction in 1960. In the third part of the talk I will discuss a new variational approach to the equations, specific to four dimensions, which seemingly doesn’t suffer from the same obstacles. Only time will tell whether this new approach can lead to the discovery of new solutions to Einstein's equations… In the talk I will make as few assumptions as possible about the audience’s background. As a consequence many things will be explained imprecisely and by analogy. More details can be supplied on request!