Speaker: Ellen Powell (Durham University)

Topic: Conformal welding, SLE, and critical Liouville quantum gravity

I will discuss the theory of so-called "quantum surfaces", which are a family of continuum random metric measure spaces believed to arise as scaling limits of (weighted) random planar maps. Particular attention will be given to the "critical" case, which refers to a special parameter in the model at which the definitions begin to break down. I will describe what happens when two such quantum surfaces are conformally welded according to their quantum boundary lengths, and the relationship with Schramm-Loewner evolutions and conformal loop ensembles.
The talk will be based on joint work with Juhan Aru, Nina Holden, and Xin Sun.