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.