Fachbereich Mathematik 
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Introduction to Higgs bundles, University of Hamburg, Summer Term 2018

Lecturers: Murad Alim and Florian Beck

This is an advanced graduate course for master and phd students as well as researchers who are interested in Higgs bundles. In particular the course will serve as a preparation for the GRK summer school on Higgs bundles. The course description can be found here.

A good working knowledge of complex geometry as well as familiarity with algebraic geometry are required.

Topics of the course:
1-Review of complex and Kähler geometry
2-Hyperkähler manifolds
3-Moduli of bundles
4-Higgs bundles

The lectures will take place in Geomatikum in the period from September 4th until September 7th, there will be two sessions on September 4-6 from 10:15-12 and from 13:15 to 15:00 as well as one session on September 7th from 10:15-12, all taking place in Geomatikum H3.


A good introductory reference are the lecture notes of Andrew Neitzke which can be found here.

The course is largely based on the following references:

[Mor07] Andrei Moroianu. Lectures on K ̈ahler geometry, volume 69 of London Mathematical Society Stu- dent Texts. Cambridge University Press, Cambridge, 2007.

William M. Goldman, Eugene Z. Xia, Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces

Further background material for the course can be found in:

[GH78] Phillip Griffiths and Joseph Harris. Principles of algebraic geometry. Wiley-Interscience [John Wiley & Sons], New York, 1978. Pure and Applied Mathematics.

[Wel08] Raymond O. Wells, Jr. Differential analysis on complex manifolds, volume 65 of Graduate Texts in Mathematics. Springer, New York, third edition, 2008. With a new appendix by Oscar Garcia- Prada.

Sessions this term:

Room, Time
1-Manifolds, tensors and derivatives (Alim)
Geom H3, 10:15-12:00
2-Bundles and connections (Alim)
Geom H3, 13:15-15:00
3-Riemannian and complex geometry (Alim)
Geom H3, 10:15-12:00
4-Hermitian and (hyper-)Kähler structures (Alim)
Geom H3, 13:15-15:00
5-Elements of Higgs bundles (Beck)
Geom H3, 10:15-12:00
6-Elements of Higgs bundles ( Beck)
Geom H3, 13:15-15:00
7-Elements of Higgs bundles (Beck)
Geom H3, 10:15-12:00

  Seitenanfang  Impress 2018-09-10, Murad Alim