Michel Bauer (Saclay):
The stochastic and conformal geometry of Schramm Loewner evolutions
Conformally invariant curves in two dimensions can be described from a
probabilistic viewpoint by Schramm Loewner equations. In the introductory
part of this talk, I shall explain their origin. Then I shall illustrate the
interplay between Ito's formula and the conformal geometry coded by these
equations. This is the crucial step to make the connexion between the
probabilistic approach and conformal field theory techniques, leading to
the identification of probabilistically conserved quantities with field
theoretic correlation functions. Finally, I shall explain how these conserved
quantities can be used to analyse the topology of conformally invariant curves.