Title
Non-smooth semi-Riemannian geometry
Abstract
Smooth Riemannian manifolds that satisfy lower Ricci curvature bounds are well studied and known to display remarkable properties. That motivated the generalisation of lower Ricci curvature bounds to metric measure spaces, i.e. spaces without any manifold structure. Those synthetic lower Ricci curvature bounds can particularly be used to study manifolds equipped with non-smooth Riemannian metrics. Under certain regularity assumptions, those still allow a distributional definition of lower Ricci curvature bounds.
In this talk, I will discuss some comparison results between the synthetic and the distributional approach to Ricci curvature on manifolds with non-smooth Riemannian metrics.
At the end of the talk, I will speak about recent advances in the case of Lorentzian manifolds.
The talk is based on joint work with Andrea Mondino and Clemens Sämann.
Please note that the seminar will take place in person in room 144 of Huxley Building.