2013 Niven Lecture - Yann Brenier
Topic
Fluids and optimal transport: from Euler to Kantorovich.
Speakers
Details
In 1757, Euler presented to the Berlin Academy of Sciences the basic equations of fluid mechanics. As pointed out by V.I. Arnold in 1966, the Euler equations for incompressible fluids have a very simple geometric interpretation that combines the concept of geodesics and the concept of volume preserving maps. The later concept is very simple and nothing but a continuous version of the discrete and more elementary concept of permutation. Conversely, the Euler equations have a natural discrete counterpart in terms of permutation and combinatorial optimization, which establishes a direct link with the mathematical theory of "optimal transport". This theory, that goes back to Monge 1781 and has been renewed by Kantorovich since 1942, is nowadays a flourishing field with many applications, in natural sciences, economics, differential geometry and analysis.
Additional Information
About the Niven Lectures: Ivan Niven was a famous number theorist and expositor; his textbooks have won numerous awards and have been translated into many languages. They are widely used to this day. Niven was born in Vancouver in 1915, earned his Bachelor's and Master's degrees at UBC in 1934 and 1936 and his Ph.D. at the University of Chicago in 1938. He was a faculty member at the University of Oregon since 1947 until his retirement in 1982. The annual Niven Lecture, held at UBC since 2005, is funded in part through a generous bequest from Ivan and Betty Niven to the UBC Mathematics Department.
Yann Brenier, École Polytechnique
