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.