Seminar on spin geometry

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Seminar on spin geometry

Semester
SoSe 2026

Lecturer
Bernd Ammann

Type of course (Veranstaltungsart)
Seminar

German title
Seminar über Spin-Geometrie

Contents
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\to 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 given on the webpage soon.

Literature
to come/see webpage

Recommended previous knowledge
Differential geometry

Time/Date
Tuesday, 16-18

Location
M311

Course homepage
https://ammann.app.uni-regensburg.de/lehre/2026s_spingeo_sem
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Organisational meeting/distribution of topics: Feb 10th, 14:15, for location see webpage
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Presentation: Giving a seminar talk of roughly 90 minutes

Examination (Prüfungsleistungen)

Detailed written report of the seminar talk

Modules
BSem, MV, MSem, LA-GySem

ECTS
4,5 ECTS, bei LA-GySem 6 ETCS