Tamás Titkos:
An introduction to classical optimal transport
In this lecture series, I will give a gentle introduction to the classical optimal transport problem. The main topics will be:
- Monge’s problem, basic examples demonstrating that the transport problem is ill-posed
- Kantorovich’s relaxation, the existence of optimal transport plans
- Kantorovich duality
- Brenier’s theorem on the existence of optimal transport maps
- transport-related metrics, basic properties of Wasserstein spaces
- applications in pure mathematics and in applied sciences.
I do not assume any prior knowledge of the theory. In fact, I will start from scratch, recalling some basic notions of measure and integration.