Place: AKR Meeting Room, International Centre for Theoretical Sciences (ICTS-TIFR), Bengaluru
Day and Time: Monday- 9:45 am to 11:00 am.
This reading seminar is devoted to Optimal Transport (OT), a mathematical framework at the intersection of probability, analysis, geometry, and applications. We will begin with the fundamental concepts of OT—the Monge and Kantorovich formulations, duality, and classical results—before moving on to advanced topics.
In the final part of the seminar, participants from different backgrounds will present talks on applications of Optimal Transport in their respective fields, showcasing its wide range of uses. The primary reference is Statistical Optimal Transport by Sinho Chewi, Jonathan Niles-Weed and Philippe Rigollet, supplemented by additional readings when necessary.
[SCJNPR] Sinho Chewi, Jonathan Niles-Weed, Philippe Rigollet, Statistical Optimal Transport.
[CV] Cédric Villani, Topics in optimal transportation.
[PC] Peyré G, Cuturi M., Computational optimal transport: With applications to data science. Foundations and Trends® in Machine Learning.
[FS] F. Santambrogio, Optimal transport for applied mathematicians: Calculus of variations, pdes, and modeling, Progress in Nonlinear Differential Equations and Their Applications.
[RV] R. Vershynin, High-dimensional probability.
[RTR] R. Tyrrell Rockafellar, Convex Analysis.
[NR] Nathan Ross, Fundamentals of Stein's method (arXiv:1109.1880)
[FL89] Joel Franklin, Jens Lorenz, On the scaling of multidimensional matrices, Linear Algebra and its Applications, pp. 114-115, 1989.
[Bre67] L.M. Bregman, The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, USSR Computational Mathematics and Mathematical Physics 7.3, pp. 200–217, 1967.
[Csi75] I. Csiszar, I-Divergence Geometry of Probability Distributions and Minimization Problems, The Annals of Probability 3.1, pp. 146-158, 1975.