Conférencier: Eric Woolgar, University of Alberta

Résumé/Abstract: Curvature-dimension inequalities are modifications of a Ricci curvature bound or, in the language of relativity, an energy condition. They have proved useful in applications of Fourier analysis to diffusion processes. As tools to prove theorems in Riemannian geometry and general relativity, they are often as powerful as the usual Ricci curvature bounds and can yield new results. Applications include static Einstein metrics, near-extremal-horizon geometry for black holes, and scalar-tensor gravity. I will discuss an application of a Riemannian curvature-dimension bound to black hole horizon topology, and use Lorentzian curvature-dimension bounds to prove some singularity theorems and splitting theorems. If time permits, I will discuss some new ideas of McCann that may permit extension of the Lorentzian results to a metric-measure setting.