# Eleftherios Theodosiadis: Explicit Loewner flows and their geometry

**Time: **
Fri 2022-11-25 09.00

**Location: **
Cramér room, Albano building 1

**Doctoral student: **
Eleftherios Theodosiadis

**Opponent: **
Björn Gustavsson (KTH)

**Supervisor: **
Alan Sola

### Abstract

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.