This talk will exploit the equivalence between the Schrödinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a priori estimates which are consistent in the limit when the regularization parameter goes to zero and also extends to multi-marginal optimal transport.

In particular, this duality approach provides an alternative proof of the convergence of the Sinkhorn algorithm with two marginals and show convergence of the Sinkhorn algorithm in the multi-marginal case.

Bio: Augusto Gerolin is Canada Research Chair and an Assistant professor at both, the Department of Chemistry and Biomolecular Sciences, and the Department of Mathematics and Statistics of the University of Ottawa. Previously, he was a Marie Skłodowska-Curie fellow at the Department of Theoretical Chemistry of the Vrije Universiteit Amsterdam. His research interests include Calculus of Variations, Optimisation, PDEs, Theoretical and Computational Chemistry, and Mathematical aspects of Machine learning theory.