8 – 10 April 2015

Organised in collaboration with the School of Mathematics, University of Bristol, UK

Scott Sheffield, Massachusetts Institute of Technology, USA

Scott Sheffield is a probability theorist, working on geometrical questions that arise in such areas as statistical physics, game theory and metric spaces, as well as long-standing problems in percolation theory. He received a PhD in mathematics from Stanford University in 2003 under the supervision of Amir Dembo. In 2011 he was selected for the Line and Michel Loeve International Prize in Probability, awarded by U.C. Berkeley every two years to recognise outstanding contributions by researchers in probability who are under 45 years old. In 2014 he was awarded a Simons Fellowship in Mathematics.

Chinese Dragons and Mating Trees

Based on joint work with Bertrand Duplantier and Jason Miller

What is the right way to think of a “random surface” or a “random planar graph”?  How can one explain the dendritic patterns that appear in snowflakes, coral reefs, lightning bolts, and other physical systems, as well as in toy mathematical models inspired by these systems?  How are these questions related to random walks and random fractal curves (in particular the famous SLE curves)?  How are they related to conformal matings of Julia sets?  To string theory?  To statistical mechanics?

I will address these questions over the course of three lectures. Along the way, I will introduce and explain the “quantum Loewner evolution” (QLE), which is a family of growth processes closely related to SLE, and I will explain some very recent work that uses QLE to describe the metric space structure of a canonical random surface called the Brownian map.

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