|Optimal transport for applied mathematicians|
|Time：||【Updated】Tue/Thu 15:10-17:00, 2016-08-04~ 2016-08-30 (No classes on Aug. 11)|
|Instructor：||Jian-Guo Liu [Duke University]|
|Place：||Conference Room 3, Floor 2, Jinchun Yuan West Building|
I will present a short, concise and rigorous course on the theory of optimal transport from a point view of applied mathematicians. Optimal transport has recently been developed as a one of main tools to do applied mathematics. Applications include image processing, economics, and evolution PDEs, in particular when modeling population dynamics in biology or social sciences, or fluid mechanics.
Santambrogio’s recent book will be the main reference and I will cover most part of the book. At the end, I will present a recent theory by the lecturer jointly with Bob Pego and Dejan on the connection between the optimal transport and weak solution to the incompressible Euler equations. I will also present some PDE results on semi-geotropic equations (Brenier e.t.), Vlasov-Monge-Ampere system (Brenier e.t.), and Monge-Ampere Keller-Segel equation (jointly with H. Huang).
Basic PDE, probability and real analysis
F. Santambrogio, Optimal Transport for Applied Mathematicians, Birkauser, 2016
J.-G. Liu, R.L. Pego and D. Slepcev, Euler sprays and Wasserstein geometry of the space of shapes, arXiv:1604.03387