Fachbereich Mathematik 
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PhD Seminar — Winter Term 2018/2019

This is the the website of the seminar of the PhD students of the Mathematics Department, research areas Algebra and Number Theory, Analysis and Differential Geometry and the RTG1670 of the University of Hamburg. If you want to subscribe to the mailing list please go to the mailing list's website.

This semester's topic is: Seiberg–Witten theory.



(Image source)

The seminar will be based on notes from a course taught by Kotschick and Hamilton at LMU Munich and will feature the following topics:
  • Physical and mathematical motivation of Seiberg–Witten theory;
  • Spinc and Spin structures;
  • Characteristic classes;
  • Results from index theory;
  • Moduli space of solutions of the Seiberg–Witten equations;
  • Examples and applications.

The seminar takes place on Mondays from 14:00 to 15:00 in Room 1643 (Geomatikum), except for sessions in red. These take place in Room 1528 (Geomatikum) at the same time.

Sessions this term:

Session Date Speaker Title Material covered
0 15-10-2018 Arpan Saha Prolegomenon and organisation Notes, §3.1-3.2, 6.1.2
1 22-10-2018 Danu Thung Preliminaries Notes
2 29-10-2018 Vincentas Mulevičius Spinc and Spin structures I §2.1-2.3
3 05-11-2018 Manasa Manjunatha Spinc and Spin structures II §2.4-2.5
4 12-11-2018 Manuel Araújo Characteristic classes and self-duality I §3.3-3.4
5 19-11-2018 Manuel Araújo, Sebastian Heller Characteristic classes and self-duality II §3.3-3.4
6 26-11-2018 Sebastian Heller Elliptic differential operators §4.1-4.2
7 03-12-2018 Ilaria Flandoli Seiberg–Witten equations and their symmetries §4.3-4.4
8 10-12-2018 Raffaele Caputo Linearisation and Banach manifolds I §5.1
9 07-01-2019 Áron Szabó Linearisation and Banach manifolds II §5.1-5.3
10 14-01-2019 Martin Vogrin Moduli space of SW solutions §5.3-5.4
11 21-01-2019 Arpan Saha Tranversality and compactness §5.5
12 28-01-2019 Tim Gabele K3 surfaces and the 4-torus §6.2-6.3.1
13 07-02-2019 Daniel Bryan Einstein and Kähler–Einstein metrics §6.3.2-6.3.3
14 14-02-2019 Danu Thung More applications §6.4
21-02-2019 Final reckoning

Literature:

Organisers: Sebastian Heller, Arpan Saha, and Danu Thung.



Previous seminars:     Winter term 2013     Summer term 2014     Winter term 2014     Summer term 2015     Winter term 2015     Summer term 2016     Winter term 2016     Summer term 2017     Winter term 2017     Summer term 2018


 
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