# Part III - Schramm--Loewner Evolutions

## Lectured by J. Miller, Lent 2018

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# Contents

- V Full version
- 0 Introduction
- 1 Conformal transformations
- 1.1 Conformal transformations
- 1.2 Brownian motion and harmonic functions
- 1.3 Distortion estimates for conformal maps
- 1.4 Half-plane capacity
- 2 Loewner's theorem
- 3 Review of stochastic calculus
- 4 Phases of SLE
- 5 Scaling limit of critical percolation}\label{sec:percolation
- 6 Scaling limit of self-avoiding walks}\label{sec:saw
- 7 The Gaussian free field}\label{sec:gff