Dario Cordero-Erausquin: Convexity, duality and heat diffusion

Motivated by a semi-group approach to the Blaschke-Santalo inequality, we will discuss how log-concavity and duality (in the form of the Legendre transform) evolve along Gaussian diffusions.
Based on two joint works with Nathael Gozlan, Shohei Nakamura, Hiroshi Tsuji and M. Fradelizi, D. Langharst.