Geometric function theory and quasiconformal maps: Lecture 1

The course will introduce students to basic concepts and techniques in geometric function theory and quasiconformal mapping of relevance in random conformal geometry. Topics include: distortion estimates for conformal maps, extremal length, harmonic measure and Brownian motion, the Loewner equation, the Beltrami equation, the geometric and analytic definitions of quasiconformal map, basic properties of quasiconformal maps, applications such as Teichmuller theory and complex dynamics.

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