Mathematical and Physical Aspects of Stochastic Loewner Evolutions

Abstract:

Since its introduction in 1999 in probability theory, Stochastic Loewner Evolutions (SLE) have steadily become more and more interconnected with different branches of mathematics and physics. SLE as originally conceived, describes random growing compact planar sets, that are invariant under conformal mappings and that can be parametrised by simple random curves.

So, the intimate connection with Conformal Field Theory (CFT) proved to be very fruitful, as it revealed deep links to representation theory of infinite Lie algebras, e.g., the Virasoro algebra, but also to complex algebraic geometry, and here in particular to moduli spaces of Riemann surfaces.

In this talk we are going to give an overview of part of the above mentioned relations and results.