Topics in Optimal Transport, High Dimensional Probability and Generative Modeling

Probability flows play an important role in the theory and applications of high-dimensional probability. The idea is to start with an easy probability measure (say a Gaussian) and gradually deform it into a complicated probability measure of interest. These types of techniques are useful in studying properties of probability measures (e.g., functional inequalities), in studying the problem of optimal transport, and in generative modeling via techniques such as flow matching and diffusion models. The course will cover topics such as the basics of probability flows, (entropic) optimal transport, basics of stochastic differential equations, and the applications of these tools to generative modeling.