Luca Rizzi

Motivated by the study of synthetic Ricci curvature bounds on singular spaces, We introduce a concept of dimension for metric measure spaces, called "geodesic
dimension", which is related with the asymptotic behavior of geodesic homotheties. We show that the geodesic dimension provides a lower bound for the best N such that the Ohta
measure contraction property MCP(K,N) can be satisfied. Moreover, this lower bound is optimal for the case of corank 1 Carnot groups (the Gromov tangent cone of corank 1
sub-Riemannian structures), extending a well known result of Juillet for the Heisenberg group. If time allows, we discuss some open problems.