Recently, a beautiful convergence of different areas of mathematics has occurred. Developments in fields, such as Free probability, Random Matrices, Rough Paths theory, and numerical methods for (partial/stochastic) differential equations, share common algebro-combinatorial formalisms. Over time it became clear that on the one hand different classes of set partitions related to cumulants and moments, and Hopf and (pre-/post-)Lie algebraic structures on the other hand are central in these advancements. As a result new interactions between combinatorial algebra and these fields has emerged.
The two weeks research school New interactions of Combinatorics and Probability addresses graduate and early PhD students. The school consists of three main lecture series. Two courses on Free Probability and Random Matrices (6hrs each), and one course on Rough Paths (6hrs). The goal is to make participants acquainted with the basic notions, motivations and examples underlying the aforementioned subjects. These fields are among the most active research areas in modern mathematics. Two complementary lecture courses (4hrs each) focus on related aspects in modern stochastic calculus and numerical methods for differential equations. Furthermore another lecture course (6hrs) shall provide the basic background in advanced enumerative and algebraic combinatorics.
In the second week the advanced parts of the main lectures shall be complemented by four extended research talks (2hrs each) focusing on recent developments in the fields of free probability, random matrices, stochastic partial differential equations and rough paths, as well as their interactions.