General description

The 18^th Lluís Santaló Research Summer School will take place from Monday 17 to Friday 21 in July 2017. Its central topics will be Algebraic and Combinatorial Methods in Stochastic Calculus. The school will bring together experts in algebraic combinatorics, stochastic differential systems, rough paths theory, the theory of regularity structures, and free probability theory, to present cutting edge introductory lectures on the fruitful interplay of research in these frontier areas of modern mathematics. The unifying link between these lectures are computational, combinatorial and algebraic structures common to these disciplines. The one-week school will consist of four lecture series, one course of 3+3 hours and three courses of 5 hours each. The school will convey the basic ideas, motivations and methods, and thereby prepare a new generation of young students to make their first steps into research at the interfaces between the aforementioned areas.

In recent years, progress has been made in the understanding of algebraic and combinatorial structures underlying several exciting advancements in modern mathematics research. This includes in particular stochastic calculus considered from the point of view of rough paths theory and free probability theory. In this respect, Hopf and Lie algebraic structures have reshaped the field of algebraic combinatorics, and turn out to be crucial in the context of applications in the aforementioned areas.