Abstract:

In this talk, I will introduce the class of “linear transfers” between probability measures. This class contains all cost minimizing mass transports, including “martingale mass transports”. It also contains the “Schrodinger Bridge” associated to a reversible Markov process, and the “weak mass transports” of Talagrand, Marton, Gozlan and others. However, what motivated us to develop the concept are the stochastic mass transports in their various forms. We also introduce the cone of “convex transfers” which in addition to linear transfers, include any p-power of a linear transfer, but also the logarithmic entropy, other correlations functionals, as well as the Donsker-Varadhan information. The ultimate goal: Stochastic Weak KAM theory.

Introduction of the speaker:

Professor Nassif Ghoussoub obtained his Doctorat d’état in 1979 from the Université Pierre et Marie Curie in Paris, France. His present research interests are in non-linear analysis and partial differential equations. He is currently a Professor of Mathematics, and a “Distinguished University Scholar” at the University of British Columbia.

He was the founding Director of PIMS (Pacific Institute for the Mathematical Sciences) for the period 1996-2003, a co-founder of the MITACS Network of Centres of Excellence (Mathematics of Information Technology and Complex Systems) and a member of its Board of Directors for the periods 1998-2003 and 2008-2016. He is also the founder of BIRS (Banff International Research Station) and has been its Scientific Director since 2004. In June 2011, he became the Scientific Director of the MPrime network of Centres of Excellence. He also served as an elected member of the Board of Governors of the University of British Columbia for the period 2008-2014.

He was elected Fellow of the Royal Society of Canada in 1993, and was appointed Officer of the Order of Canada in December 2015.