Pavlos Tsatsoulis: Lie algebras and Hopf algebras for beginners towards applications to singular SPDEs

  • Lecturer: Pavlos Tsatsoulis
  • Keywords: Lie algebras, Hopf algebras, singular SPDEs
  • Prerequisites: Basic algebra, some knowledge of (S)PDE theory is recommended

Abstract

In this series of lectures I intend to give an introduction to Lie algebras and Hopf algebras. My main motivation comes from the theory of singular SPDEs and, in particular, Hairer's theory of regularity structures, where Lie algebras and Hopf algebras appear. The plan will be as follows. In the first main part I will introduce the basics of Lie algebras and Hopf algebras, using a beginner's approach to target non-specialists on the topic. In the second part I will try to give an idea on how these purely algebraic concepts can be applied in the theory of singular SPDEs, possibly by considering specific examples like the \(\Phi^4_d\)-model or the KPZ equation. For this part, knowledge of (S)PDE theory is recommended.
02.06.2020, 02:30