In the fall of 2024 the applied analysis faculty will be organizing a working group with the goal of learning optimal mass transport. Faculty, grad students and postdocs take turns presenting material, starting from fundamental topics and progressing to research papers at the forefront of current research in OT. All are welcome to attend and participate!
If you have any questions about the working group, please contact one of Will Feldman, Braxton Osting, Katya Epshteyn, or me.
This is the webpage for the working group, to record our readings, notes that might be generated, etc. It will be updated weekly; below is a tentative plan, and the exact schedule will be updated as we go, in order to allow for greater flexibility in the lectures.
When: Mondays, 2-3pm. Where: LCB 222.
References: Textbooks: Optimal mass transportation on Euclidean spaces, Francesco Maggi [M]
Optimal mass transportation for applied mathematicians, Filipo Santambrogio [S]
Course notes on entropic optimal transport by Marcel Nutz
Notes on optimal mass transport by Lawrence C. Evans.
references to specific research papers will be posted here.
9/9: Organizational meeting; Will Feldman gave an overview lecture.
9/16: I gave an example-based lecture on background material on the calculus of variations, trying to connect it to some formulations of OT.
discrete problems and c-cyclical monotonicity. (Dongwan)
The Kantorovich formulation (Conrad)
Brennier McCann's theorem (Zhonggan)
The Benamou-Brenier dynamic formulation of optimal transport and the geometry of the Wasserstein space (Will)
JKO and gradient flows (Batuhan)
Entropic OT and Sinkhorn's algorithm (Kerrek)
Applications of OT to topological data analysis and its applications (Bei Wang and members of her group)
Computational aspects of optimal transport (Braxton and Zijie)