Focus topic: Differential Geometry and Geometric Analysis

Differential manifolds provide higher dimensional generalizations of surfaces. They appear in a very natural manner n many areas of mathematics and physics. On a differential manifold or more generally on a geodesic metric space, one investigates geometric and analytic quantities and concepts, such as geodesics, the curvature of Riemannian metrics or potential theory, and also group actions on such spaces.Of particular interest are connections between such quantities and global, topological properties of the underlying manifold, which are investigated in differential geometry and geometric analysis.

This picture shows the famous Zoll surface: all geodesics are closed and of equal length.

The focus topic Differential Geometry and Geometric Analysis is closely related to topology, analysis, stochastics, group theory and to physic, e.g. Einstein's general relativity. A good background in algebra is helpful.

Courses for the specialisation in Differential geomtry (DG) and Geometric structrues (GS)

Winter semester 2019/2020

  • Prof. Dr. Christoph Böhm: Differential geometry II (Typ I, DG)
  • Prof. Dr. Jochen Lohkamp: Geometric analysis, potential theory (Typ I, GS)

Summer semester 2020

  • Prof. Dr. Christoph Böhm: Ricci flow (Type II, DG)
  • Prof. Dr. Linus Kramer: Topological groups (Type I, II, GS)
  • Prof. Dr. Jochen Lohkamp: Selected topics on differential geometry (Type II, GS)

Prerequisites for Geometric analysis: Analysis 1-3. Not necessary but useful are basics in partial differential equations and complex analysis.

Prerequisites

A course in differential geometry with the following content:

Riemannian manifolds, geodesics, Levi-Civita-connection, Lemma of Gauß, Theorem of Hopf-Rinow, curvature tensor, first and second variation formula, Lemma of Synge, Theorem of Bonnet-Myers, submanifolds, Gauß equation, Theorema egregium, Jacobi fields, Theorem of Hadamard-Cartan.