Title: Introduction to Schramm-Loewner evolution (SLE)

Abstract:

Random planar curves arise as interfaces in models of 2d statistical 
physics. There has been a conjecture that at criticality these models 
are, 
in some sense, conformally invariant. To study this Oded Schramm 
introduced SLE in 1999. SLEs are a family of random, 
non-self-intersecting, planar curves that are characterized by two 
properties: conformal invariance and Markov property. In this talk I 
will 
introduce Loewner equation and Schramm's principle leading to the 
definition of SLE. If time permits I will present some properties of SLE 
and give an example of a typical calculation enabled by the technique.