# On the interplay between horizontal and vertical derivation

## Nicola Gigli

### (IMJ - UPMC)

Date: Oct 10, 2011, time: 15:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. I will talk about some recent developments on the interplay between the $L^2$ and $W_2$ geometries. Results include the possibility of studying the continuity equation in a genuine metric framework, and the identification of the heat flow as gradient flow in spaces with Ricci curvature bounded from below.