Unified Synthetic Ricci Curvature Lower Bounds for Riemannian and Sub-Riemannian Geometries

Explore a groundbreaking approach to unifying Riemannian and sub-Riemannian geometries through synthetic Ricci curvature lower bounds in this 45-minute conference talk by Davide Barilari at the Erwin Schrödinger International Institute for Mathematics and Physics. Delivered as part of the Workshop on "Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension," delve into recent advances in metric measure spaces and sub-Riemannian geometries that suggest the possibility of a comprehensive framework. Examine the proposed new approach based on the study of gauge metric measure spaces, aiming to achieve a "great unification" of these geometric theories. Gain insights into this collaborative work with Andrea Mondino and Luca Rizzi, pushing the boundaries of our understanding of curvature in diverse geometric settings.