Seminar on spin geometry
Prof. Bernd Ammann,
Content of the Seminar
The seminar starts with an introduction to spin structure, spinors and Dirac operators. The Dirac operator is a natural operator associated to a Riemannian or Lorentzian manifold, which is roughly a square root of a Laplace operator (on a Riemannian manifold) or a wave operator (on a Lorentzian manifold). The origin of this operator is from particle physics, but we are mainly interested in geometric applications.
In the main part of the seminar we will present several original articles with geometric applications. The topics will be fixed within the next days and also still flexible for wishes of the participants, but will be close to the following
subjects:
- the Weierstrass representation of minimal surfaces and surfaces of constant mean curvature in space,
- its modification in 3+1 dimensions and relations to the constraint equations in general relativity
- prescribing mean curvature for conformal maps S2→ ℝ3
- positive scalar curvature
- nonnegative scalar curvature and its relations to special holonomy
- recent related theorems on compact manifolds with boundary
- the positive mass theorem in physics and space-time generalization
- the kernel of the Dirac operator
More details will be visible in the program (pdf file with list of talks) below.
Requirements
Differential geometry
Time and Place
Tuesday, 16-18, M311
Organisational meeting
Monaday, Feb 9th, 14:15, in M311, Attention Date has changed!
Program
A first preliminary version of the program of the seminar is available here. It already shows the range of possible topics. The precise topics and their orders still have to be worked out, and this will also depend on the participants.
Registration
Come to the organisational meeting (see above).
Related web pages
Bernd Ammann, 12.02.2026
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