Ricci flow emerging from singular spaces with bounded curvature

A metric flow (M, g(t))(0,T ) on a compact manifold M sat- isfying the Ricci-flow equation is said to have a metric space (X,d) as its initial condition if (X, d) is the Gromov-Hausdorff limit of (M, dg(t)) as t → 0. The question of what assumptions on (X,d) guarantee the existence of a Ricci flow (M, g(t)) with (X, d) as its initial condition, and how further regularity assumptions on (X, d) and (M, g(t)) can improve the convergence, is among the primary problems in this area. In this talk, I will present results on the existence and uniqueness of a solution to the Ricci flow, where the initial condition is a compact length space with bounded curvature, specifically a space that is both Alexandrov and CAT, and discuss how these conditions strengthen the convergence. This work is joint with Diego Corro and Adam Moreno.