In his 2017 Bourbaki seminar, Villani proposed as open problem to obtain a ”Great unification” of Riemannian, Finslerian and Sub-Riemannian synthetic Ricci lower bounds. The goal of the talk is to report on joint work with Barilari (Padova) and Rizzi (SISSA) on the topic.

Bio: Andrea Mondino is an Italian mathematician. Mondino earned his doctorate from SISSA-Trieste in 2011, under the supervision of Andrea Malchiodi. He then had several post doc positions: in Scuola Normale Superiore-Pisa (in the group of Luigi Ambrosio), in ETH-Zurich (ETH fellow, in the group of Tristan Rivière) at MSRI-Berkeley (Hunuke Fellow during a six month program) and University of Zurich, He then had his first permanent position as Assistant Professor at the University of Warwick in 2015, where he was promoted to Associate Professor and to Reader. In 2019 he moved to the University of Oxford where he is Professor of Mathematics since 2022. In his research, he studies problems arising from geometry or theoretical physics by using analytical methods, such as partial differential equations or optimal mass transport. He obtained several recognitions such as an ERC Starting Grant, a Whitehead Prize from the London Mathematical Society, a Bartolozzi Prize from the Italian Mathematical Union.