Fluids and optimal transport: from Euler to Kantorovich

授课人:Yann Brenier

机构:Pacific Institute for the Mathematical Sciences(PIMS)

关键词: Scientific;    Mathematics;    Permutation and combinatorial optimization;   

加拿大|英语

【 摘 要 】

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.

【 授权许可】

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