A session on the harmonic map flow, starting from the original article of Struwe (On the evolution of harmonic mappings of Riemannian surfaces. Comment. Math. Helv. 60, 558-581 (1985). …

Some materials are neatly organized, like iron or nickel, while others are a complete mess, like spin glasses. It is the latter that I propose we examine. We will define a mathematical framework that is now fairly …

I will start by discussing a famous open problem in combinatorics: the enumeration of meanders. This problem can be formulated as an optimization problem on the set of non-crossing partitions, that we shall in turn …