An algebraic perspective to Schramm-Loewner evolutions
Mon, Oct. 08th 2007, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Schramm-Loewner evolutions (SLE) are random, conformally invariant
curves that describe continuum limits of interfaces in 2-d statistical
physics at criticality. After a brief introduction to SLEs, I will
discuss an approach to SLEs with quantum physics flavour, \`a la Bauer
and Bernard. A closer study of this approach reveals natural appearance
of many kinds of representations of Virasoro algebra, not only
highest weight representations.
To illustrate what this algebraic point of view teaches us about SLEs,
I'll show how to obtain partial results of two well-known SLE questions:
reversibility of chordal SLE trace and ``Duplantier duality'' for SLEs.