Commutative and non-commutative cumulants and applications

Combinatorics of Laver tables

I will give two talks on cumulants, which are combinatorial quantities allowing to define notions of independence in probabiity, either classic or non-commutative. The combinatorics of cumulants is rich and focuses on several classes of partitions (set partitions, noncrossing partitions or interval partitions for example). I will give also applications of these notions to random matrix theory and physics.

The last talk will be about Laver tables, which are finite sets endowed with a left distributive operation. They have been invented in logic, in the theory of sets with large cardinals, but can be studied from a completely finite and combinatorial point of view. Although their definition is very simple and elementary they turn out to be quite complex objects with fascinating combinatorial properties.