Maths meets Stats

Speaker: Mattia Magnabosco (Newton Fellow, Maths)
Title: Synthetic Ricci curvature bounds in sub-Riemannian manifolds
Abstract: In Riemannian manifolds, a uniform bound on the Ricci curvature tensor allows to control the volume growth along the geodesic flow. Building upon this observation, Lott, Sturm and Villani introduced a synthetic notion of curvature-dimension bounds in the non-smooth setting of metric measure spaces. This condition, called CD(K,N), is formulated in terms of the optimal transport interpolation of measures and consists in a convexity property of the Rényi entropy functionals along Wasserstein geodesics. The CD(K,N) condition represents a lower Ricci curvature bound by K and an upper bound on the dimension by N, and it is coherent with the smooth setting, as in a Riemannian manifold it is equivalent to a lower bound on the Ricci curvature tensor. However, the same relation between curvature and CD(K,N) condition does not hold for sub-Riemannian (and sub-Finsler) manifolds. 

Speaker: Rebecca Lewis (Florence Nightingale Bicentenary Fellow, Stats)
Title: High-dimensional statistics
Abstract: Due to the increasing ease with which we collect and store information, modern data sets have grown in size. Whilst these datasets have the potential to yield new insights in a variety of areas, extracting useful information from them can be difficult. In this talk, we will discuss these challenges.