Thomas Walpuski

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.

10.11.2020
Thomas Walpuski
Bundles, connections, and curvature
Thomas' notes
17.11.2020
Niklas Martensen
Yang–Mills functional, ASD instantons, and the BPST instanton
Niklas' notes
24.11.2020
Solveig Milena Hepp
Sobolev spaces, Fredholm theory, and elliptic theory
Solveig's notes
01.12.2020
Douglas Schultz
Uhlenbeck's gauge fixing theorem
Douglas' notes
08.12.2020
Shubham Dwivedi
Uhlenbeck's removable singularities theorem
Shubham's notes
15.12.2020
Naageswaran Manikandan
The compactness problem for ASD instantons
Naageswaran's notes
05.01.2021
Milica Đukić
Taubes' gluing theorem
Milica's notes
12.01.2021
Adrian Philipp Dawid
Overview of the topology of 4–manifolds
Adrian's notes and slides
19.01.2021
Joshua Egger
Construction of the moduli space of ASD instantons
Joshua's notes
26.01.2021
Thomas Walpuski
The collar theorem
Thomas' notes
02.02.2021
Michael Rothgang
Analysis of reducibles and conclusion of the proof of Donaldson's theorem
Michael's notes
09.02.2021
Gorapada Bera
The Narasimhan–Seshadri theorem
Gorapada's notes