# Structure of Non-smooth spaces with Ricci curvature lower bounds

**Date**: Wednesday 1 March 2017, 15:00 – 16:30**Location**: Roger Stevens LT 12 (10M.12)**Type**: Geometry, Seminars, Pure Mathematics**Cost**: Free

#### Andrea Mondino, University of Warwick. Part of the geometry seminar series.

The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80s and was pushed by Cheeger and Colding in the '90s who investigated the structure of the spaces arising as Gromov-Hausdorff limits of smooth Riemannian manifolds satisfying Ricci curvature lower bounds. A completely new approach via optimal transportation was proposed by Lott-Villani and Sturm almost ten years ago; with this approach one can a give a precise meaning of what means for a non smooth space to have Ricci curvature bounded from below by a constant. This approach has been refined in the last years by a number of authors and a number of fundamental tools have now been established (for instance the Bochner inequality, the splitting theorem, etc.), permitting to give further insights in the theory. In the seminar I will give an overview of the topic with emphasis on the structure of such non smooth spaces (i.e. tangent cones and rectifiability properties).

**Andrea Mondino, ***University of Warwick*