Georgia Institute of Technology College of Sciences

Stochastic Loewner evolution (SLE) introduced by Oded Schramm is a breakthrough in studying the scaling limits of many two-dimensional lattice models from statistical physics. In this talk, I will discuss the proofs of the reversibility conjecture and duality conjecture about SLE. The proofs of these two conjectures use the same idea, which is to use a coupling technique to lift local couplings of two SLE processes that locally commute with each other to a global coupling. And from the global coupling, we can clearly see that the two conjectures hold.