This is the webpage for a directed reading program (DRP) I am leading during MIT's Independent Activities Period (IAP 2020). The subject is high-dimensional statistics and an introduction to optimal transport.

**[PC] PeyrÃ© and Cuturi,***Computational Optimal Transport*(2019).**[W] Wainwright,***High-Dimensional Statistics*(2019).- [BBI] Burago, Burago, and Ivanov,
*A Course in Metric Geometry*(2001). - [DPV] Dasgupta, Papadimitriou, and Vazirani,
*Algorithms*(2008). - [LPW] Levin, Peres, and Wilmer,
*Markov Chains & Mixing Times*(2009). - [MM] Moore and Mertens,
*The Nature of Computation*(2011). - [S] Santambrogio,
*Optimal Transport for Applied Mathematicians*(2015). - [V] Villani,
*Topics in Optimal Transportation*(2003).

- (preparation) A preview of high-dimensional statistics. [W] 1.1-1.5.
- (1/6) Total variation distance and couplings. Monge problem and Kantorovich problem. [LPW] 4.1-4.2, [PC] 2.1-2.3.
- (1/8) Metric properties of the Wasserstein distance and examples. Introduction to linear programming (LP) duality. [PC] 2.4, 2.6, [DPV] 7.4.
- (1/10) Kantorovich duality, c-transforms, complementary slackness. [PC] 2.5, 3.1-3.3, 5.1.
- (1/13) The transportation polytope and its vertices. Simplex algorithm. [PC] 3.4-3.5, [MM] 9.4.1-9.4.3.
- (1/15) Entropically regularized optimal transport and Sinkhorn's algorithm. [PC] 4.1-4.2.
- (1/17) W1 optimal transport on metric spaces and its dual. Lipschitz functions and concentration of measure (blow-up). T1 transportation inequality. [PC] 6.1-6.3, [W] 3.2.1-3.2.2, 3.3.1-3.3.2.
- (1/20) Holiday.
- (1/22) Continuity equation. Geodesics in Wasserstein space; McCann interpolation and Benamou-Brenier formula. Displacement/geodesic convexity. [PC] 7.1, 7.5, [V] 5.1.3-5.2.1, 8.1.2-8.1.3.
- (1/24) Survey of ``distances'' between probability distributions: divergences, integral probability metrics, kernels. [PC] 8.1-8.3.
- (1/27) Wasserstein barycenters and multi-marginal optimal transport. [PC] 9.2, 10.1, [S] 5.5.5.
- (1/29) Distances between metric spaces: Lipschitz distance, Hausdorff distance, Gromov-Hausdorff distance, Gromov-Wasserstein distance. [PC] 10.6, [BBI] 7.2-7.3.