Synthetic nonnegative cross-curvature lifts to the Wasserstein space

par François-Xavier Vialard

lundi 22 avr. 2024, 11:00 → 12:00 Europe/Paris

1016 (Université Paris-Cité (campus Grands Moulins))

In this talk, we insist on the concept of nonnegative cross-curvature and its synthetic definition for a general cost on a product space. Then, by using a formal argument we show why one can expect that such a property should be also true for the Wasserstein space. Then, we give examples of cost satisfying this synthetic nonnegative cross-curvature, in particular a new one with the Bures-Wasserstein case. We extend the result to the case of unbalanced optimal transport and show some potential applications.