The aim of the project is to study the role of certain algebraic objects, as Lie algebras, Hopf algebras, pre-Lie algebras, in the recent developement in quantum field theory, in the theory of pseudo-differential operators and in probability theory. More precisely, the lecture will cover the following subjects:
- Application of combinatorial Hopf algebras in renormalization theory, quantum field theory and probability theory.
- Combinatorial and probabilistic properties of heaps and their applications in physics.
- Operad theory and their applications in deformation theory.
- Virasoro algebras and supersymmetry.
- Pseudo-differential operators and pre-Lie algebras.