Isaia Nisoli: An Introduction to Approximation of Invariant Measures and the distances involved

Abstract. In this talk I will give an introduction to the problem of approximating invariant measures for one dimensional maps.
In particular I will try to explain what are the main methods used and approximation distances used in the
case of piecewise expanding maps of the interval and the role played by regularity to get stronger approximations.
I will also introduce the Wasserstein-Kantorovich distance and explain in which way this would be a natural
distance for approximations and the reasons why our approximation strategy is not working.