Title: Algebraic structures for singular SPDEs

授课人（Speaker）：Yvain Bruned，Université de Lorraine

授课地点(Location)： 吉林大学数学楼第五研讨室

短课时间：2025年7月6-10日

Abstract: This course aims to give an overview of the algebraic structures that appear in the context of singular stochastic partial differential equations (SPDEs). They are at the core of the theory of Regularity Structures for providing solutions to singular equations via a local expansion. This local expansion needs various renormalisations for constructing stochastic iterated integrals which are new monomials. One has a lot of algebraic structures on this expansion that we will present in this course.

The course will be divided into four lectures with the following title:

(1) 16:00-17:00, July 6, 2025, Decorated trees for singular SPDEs

(2) 16:00-17:00, July 7, 2025, Positive and negative renormalisation

(3) 16:00-17:00, July 9, 2025, Pre-Lie, Novikov and Post-Lie algebras in Regularity Structures

(4) 16:00-17:00, July 10, 2025, Homological tools for the chain rule symmetry

报告人简介：Yvain Bruned is currently a Professor of Mathematics at the Université de Lorraine. In 2024, he won the Frontiers of Science Award in Mathematics for the paper "Algebraic renormalisation of regularity structures" co-written with Martin Hairer and Lorenzo Zambotti.