Speaker: Yilin Wang

Title: Coupling theorems for finite energy curves

Abstract: 
The Loewner energy defined for Jordan curves is the action functional of 
Schramm-Loewner evolution, and is also the SLE's large deviation rate 
function with vanishing parameter. We showed recently that a Jordan curve 
has finite energy if and only if it is a Weil-Petersson quasicircle, which 
is of physics interest providing one of the frameworks for non-perturbative 
formulation of string theory. In this talk we present two identities that 
relate the Loewner energy to the Dirichlet energy of ambient fields. 
They are deterministic analogs of both the welding and flow-line couplings 
of SLEs with the Gaussian free field on the level of action functionals. 
We apply these results to show that the operation of arclength isometric 
welding of two finite energy domains is sub-additive in the energy and that 
the energy of equipotentials in a simply connected domain is monotone. 
This is a joint work with Fredrik Viklund.