Conveners
Inaugural lecture: Integrable combinatorics
- Philippe Di Francesco
Description
Physics has always provided insights and inspiration into new mathematics. We will concentrate here on Combinatorics, namely the art of counting objects
in classes, and follow guidance from Statistical physics that attaches probability weights to those objects and tries to tackle fundamental questions such as correlations or thermodynamic behavior. Symmetries of the systems studied can sometimes drastically simplify them, and in the best cases lead to exact solutions (i.e. exact counting, or exact asymptotics of such counts). Discrete or continuous integrable systems have enough symmetries to guarantee the existence of exact solutions. In this lecture, we will explore and solve a number of combinatorial integrable problems, in relation to various areas of mathematics: random geometry, random surfaces, cluster algebras, etc.
