Algebraic & Geometric Structures in Stochastic Calculus

In recent years, algebraic, geometric, and analytical investigation, coupled with stochastic methods have lead to important new developments in probability theory.

This project aims at both deepening and extending these advancements, by fostering interactions between the following particular directions: symmetry and invariance properties considerations, including those of the underlying spaces; progress in stochastic analysis related to interconnections between quantum field theory, Wick calculus, renormalization and singular SPDEs; advances in the study of Hopf algebras and related recent algebra-geometrical structures, and their applications to renormalization theory, the theory of regularity structures, and controlled rough paths; further development of a recently proposed notion of Grassmann probability theory which allows for a new path for extending concepts from probability theory, calculus of variation, stochastic analysis, and singular PDEs to an anticommutative (Fermionic) context.