Seminar: Gauge Theory/Eichtheorie (Wintersemester 2020/21)
In the winter semester 2020/21,
I will ran a seminar on gauge theory.
Gauge theory is vast topic with a long history and an area of a lot of current research.
This seminar covered only a small but important part of this subject.
The plan for this seminar was to build up the geometric and analytic foundations of gauge theory in dimension four, and to discuss the proof of Donaldson's diagonalization theorem.
Bundles, connections, and curvature
Yang–Mills functional, ASD instantons, and the BPST instanton
Solveig Milena Hepp
Sobolev spaces, Fredholm theory, and elliptic theory
Uhlenbeck's gauge fixing theorem
Uhlenbeck's removable singularities theorem
The compactness problem for ASD instantons
Taubes' gluing theorem
Adrian Philipp Dawid
Overview of the topology of 4–manifolds
Construction of the moduli space of ASD instantons
The collar theorem
Analysis of reducibles and conclusion of the proof of Donaldson's theorem
The Narasimhan–Seshadri theorem