6 February 2025
3:30pm CET
STEFAN SUHR
(Ruhr-University Bochum, Germany)
Title: Optimal Transport in Lorentzian Geometry
Abstract: In recent years the theory of optimal transportation has made an impact on Lorentzian geometry, mainly through synthetic definitions of timelike Ricci curvature bounds for Lorentzian manifolds and Lorentzian length spaces. But there are also other aspects of Lorentzian optimal transport relevant to general relativity. I will give an overview of the basic ideas of Lorentzian optimal transport and recent results. Further I will indicate some open problems in this context.
6 March 2025
3:30pm CET
SIMON BRENDLE
(Columbia University, USA)
Title: Systolic inequalities and the Horowitz-Myers conjecture
Abstract: I will discuss joint work with Pei-Ken Hung on the
Horowitz-Myers conjecture in dimension at most 7. Our approach relies on a new geometric inequality. For a Riemannian metric on B2xTn-2 with scalar curvature at least -n(n-1), this inequality
relates the systole of the boundary to the mean curvature of the boundary.