Valérie Berthé, IRIF, CNRS et Université de Paris

Slides in English and presentation in French (or English if required).

The videos: part 1, and part 2.

The object of combinatorics is to count objects.

Its relations with computer science are natural but is scope goes much beyond; combinatorics is ubiquitous and it has a wide range of applications, in particular in statistical physics.

We will first evoke several instances of combinatorics (enumerative, geometric, analytic, algebraic, etc.) and discuss several related fields. We will then focus on word combinatorics and its relations with formal languages, and on the notion of quasiperiodic order in connection with the study of tilings and quasicrystals.