Research School CIMPA "Algebra, Combinatorics and Physics"
Valparaíso, January 20-31 2014
(Facultad de Ingeniería, Universidad de Valparaíso - Avenida Brasil 1786, Valparaíso, Chile)

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 :

a). Application of combinatorial Hopf algebras in renormalization theory, quantum field theory and probability theory.
b). Combinatorial and probabilistic properties of heaps and their applications in physics.
c). Operad theory and their applications in deformation theory.
d). Virasoro algebras and supersymmetry.
e). Pseudo-differential operators and pre-Lie algebras.