## Lectures

Lectures (48h) are on Tuesdays and Thursdays.

Registration for the course is in Korppi.

## Contents

Monge and Kantorovitch formulations of optimal mass transportation, existence and uniqueness of optimal transport maps, Wasserstein
distance, brief introduction to functionals and gradient flows in Wasserstein spaces, Ricci curvature lower bounds in metric spaces using
optimal mass transportation.

## Passing the course

Passing the course requires passing the final exam. The first opportunity to take the exam is on 3.12.2014.
The second one is on 16.12.2014

## Literature

**Lectures are largely based on:**

L. Ambrosio and N. Gigli, **A User's Guide to Optimal Transport** in *Modelling and Optimisation of Flows on Networks, Lecture
Notes
in Mathematics*, 2013, pp 1-155. http://cvgmt.sns.it/paper/195/

**Another good book with extensive comments on the literature:**

C. Villani, **Optimal Transport - Old and New** http://cedricvillani.org/wp-content/uploads/2012/08/preprint-1.pdf

**For more on Gradient Flows:**

L. Ambrosio, N. Gigli and G. Savaré, **Gradient Flows in Metric Spaces and in the Space of Probability Measures**

## Lectures

Lecture notes

Last modified: 27.11.2014