Title: Conformally invariant random shapes and Schramm-Loewner evolution
Speaker: Dapeng Zhan
Speaker Info: MSU
Special Note: Note unusual time.
Many two-dimensional lattice models were observed by statistical physicists to satisfy conformal invariance when their meshes are very small. These conjectures were solved using the newly developed Schramm-Loewner evolution (SLE) introduced by Oded Schramm in 1999. The SLE process generates a random fractal curve growing in a plane domain, and its behavior depends on a positive parameter. The SLE with different parameters are proved to be the scaling limits of different lattice models. In this review talk I will briefly talk about the definition of SLE, several lattice models which converge to SLE, and my research on SLE.Date: Monday, February 13, 2012