Teaching
Basic Courses on Complex Analysis
- Turnus: Jedes Sommersemester
- Voraussetzungen: Inhalte der Vorlesungen Analysis 1 und 2 (Bachelor).
- Inhalt: Der kanonische Stoff einer einführenden Vorlesung zur Funktionentheorie: Cauchy-Theorie, Fundamentaleigenschaften holomorpher und meromorpher Funktionen, konforme Abbildungen und der Riemannsche Abbildungssatz, konstruktive Funktionentheorie.
- When: Every winter term
- Prerequisites: A basic Complex Analysis course at the Bachelor's level
- Syllabus: Advanced topics in Complex Analysis such as Potential Theory and Geometric Function Theory
Advanced Course
Applications of methods from Complex Analysis to Harmonic Analysis, Operator Theory, Spectral Theory, Banachalgebras and Mathematical Physics, e.g.
- Spectralprojections using Cauchy's Integral Formula
- Von Neumann's Inequality
- Spectral Theorem for unbounded operator
Direct proof based on the Herglotz Formula - Hardy- and Bergman Spaces of holomorphic functions
- Invariant subspaces
Prerequisites: Introductory Course on Complex Analysis (Bachelor's level), a little functional analysis
Selected Courses on Complex Analysis
We regularly offer advanced courses (lectures, seminars, research in groups) at master's level that give an introduction to research topics of intense current interest such as
Constructive methods in Complex Analysis based on the dbar equation and methods of Harmonic Analysis with applications to Potential Theory, Topology, the inverse problem of Galois Theory (Grothendieck's dessins d'enfants) and uniformization of Riemann Surfaces.
Basics of Loewner Theory, a particularly modern topic in geometric function theory with Fields-Medals for W. Werner (2006) and St. Smirnow (2010) with applications in Mathematical Physics.
Introduction to the mathematics of Julia sets and the Mandelbrot set.
Uniformisation and Deformation of complex and conformal structures.
Prerequisites: Complex Analysis (Master) and Differential Geometry (Master)
