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Eleftherios Theodosiadis: Explicit Loewner flows and their geometry

Tid: Fr 2022-11-25 kl 09.00

Plats: Cramér room, Albano building 1

Licentiand: Eleftherios Theodosiadis

Granskare: Björn Gustavsson (KTH)

Huvudhandledare: Alan Sola

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In this Licentiate Thesis, we address problems related to partial differential equations for Loewner Theory. We study multi-slit Loewner flows in the unit disc and the upper half plane respectively. Specifically, we solve explicitly Loewner’s PDE for a particular choice of driving functions and we describe the geometry of these solutions, while we also remark a close connection of these solutions to semigroups of holomorphic self maps. To conclude, we present a short note on elementary examples of Loewner flows, driven by time-dependent densities.