Aims and scopes

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 lecture series, including courses on Free Probability and Rough Paths (6hrs each), and a course on Determinantal Processes (7hrs). 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 (5hrs) shall provide the basic background in advanced enumerative and algebraic combinatorics.

The lectures shall be complemented by seven research talks (1h 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 and related fields. In addition, two poster sessions are devoted to those participants interested in sharing their results and research projects in the topics of the school and related areas.