On the volume product of sets and functions: a survey on some of the latest results

par Matthieu Fradelizi (LAMA -Université Gustave Eiffel)

lundi 13 avr. 2026, 14:00 → 15:00 Europe/Paris

Salle Pellos (1R2-207)

I shall present the classical Blaschke-Santalo inequality and Mahler’s conjecture on the volume product of convex sets as well as their functional extensions. I shall insist on a few recent results: 

- a proof of a general Mahler’s functional form of the conjecture in dimension two obtained with Elie Nakhle, 

- a functional form of Blaschke-Santalo inequality for the Legendre transform using the heat semigroup co-authored with Dario Cordero-Erausquin and Dylan Langharst, which generalises to general functions a previous result of Nakamura and Tsuji

- the Blaschke-Santalo inequality for multiple even functions due to Nakamura and Tsuji as an application of a new type of inverse Brascamp-Lieb inequalities for even functions extending previous results of Barthe and Wolff.