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Ellen Krusell: Schramm-Loewner Evolution - A Marriage of Probability Theory and Complex Analysis

Time: Thu 2022-06-02 13.00 - 14.00

Location: KTH, 3721 and Zoom (meeting ID: 68578498723)

Lecturer: Ellen Krusell (KTH)

Abstract


The family of random planar curves known as Schramm-Loewner evolution (SLE) were introduced in 2000 by Oded Schramm. The motivation was that several random curves arising in statistical physics models were predicted to have scaling limits which statisfy conformal invariance and a domain Markov property. It was then natural to ask: is there an explicit (and useful) construction of curves statisfying both of these properties? Luckliy, as Schramm realised, the answer to this question is yes.

In this talk we will outline the story of how Schramm-Loewner evolution was introduced. We will start by discussing scaling limits and the critical percolation model. Thereafter we will discuss (deterministic) Loewner evolution, and finally, we will define and give some properties of Schramm-Loewner evolution.