Reading seminar on various topics in gauge theory
We will start discussing Seiberg-Witten gauge theory and its applications to 4-manifold topology. However, the content of the seminar will depend on the participants' interests also. Topics beyond the foundational Seiberg-Witten theory may include the proof of the Thom conjecture, symplectic 4-manifolds, glueing results along 3-tori and existence of infinitely many smooth structures on the same underlying topological 4-manifold, Seiberg-Witten theory for families. Talks will be given by (not necessarily all) participants
The seminar meets on Wednesdays at 14:00 on Zoom. Talks will last 60min + 15min approximately.
Meeting-ID: 650 6685 9285
Password: Magnetic gadgets usually always have two poles, but there are physical theories describing also some objects having just one. This is called a magnetic xxxxxxxx. The sought word is the password for the meeting. Solutions to the Seiberg-Witten equations are also named Seiberg-Witten xxxxxxxxs. (If you can't guess it email me.)
- [D] S. Donaldson: The Seiberg-Witten equations and 4-manifold topology, Bulletin of the AMS 33 (1996), 45--70
- [G] P. Ghiggini: Floer homology detects genus-one fibred knots., Amer. J. Math. 130 (2008), no. 5, 1151--1169.
- [GS] R. Gompf, A. Stipsicz: 4-manifolds and Kirby calculus, AMS Graduate Studies in Mathematics
- [Kotsch] D. Kotschick: The Seiberg-Witten invariants of symplectic four-manifolds [after C.H. Taubes], Astérisque, tome 241 (1997), Séminaire Bourbaki,exp. no812, p. 195--220
- [K] P. Kronheimer: Embedded surfaces and gauge theory in three and four dimensions, Surveys in Differential Geometry, available on his webpage
- [KM] P. Kronheimer, T. Mrowka: Monopoles and three-manifolds, Cambridge New Mathematical Monographs
- [KM2] P. Kronheimer, T. Mrowka: The genus of embedded surfaces in the complex projective plane, Mathematical Research Letters1, 797--808 (1994)
- [Mor] J. Morgan: The Seiberg-Witten equations and applications to the topology of smooth four-manifolds, Princeton University Press
- [Moo] J. Moore: Lectures on Seiberg-Witten invariants, Springer Lecture Notes in Mathematics
- [R] D. Ruberman: Positive scalar curvature, diffeomorphisms and the Seiberg-Witten invariants, Geom. Topol.5 (2001), 895--924
- [Tau] C. Taubes: Gauge theory on asymptotically periodic 4-manifolds, J. Differential Geom. 25 (1987), no. 3, 363--430.
- [Tel] A. Teleman: Introduction à la Théorie de jauge, Cours spécialisés, Collection SMF 18
List of talks and speakers (preliminary)
| Date | Topic | Speaker | Literature | Recording & Notes |
|---|---|---|---|---|
| 28.4. | Spin^c structures and the Seiberg-Witten equations | Andras Stipsicz | [K,KM,Mor,Moo,GS] | Recording |
| 5.5. | The a-priori estimate and compactness of the moduli space | Willi Kepplinger | [K,KM,Mor,Moo] | Recording , Notes |
| 12.5. | Reducibles, transversality, index theory, definition of the Seiberg-Witten invariant | Gheehyun Nahm | [Mor,Tel] | Recording , Notes |
| 19.5. | Seiberg-Witten Floer homology | Piotr Suwara | [KM] | Recording , Notes |
| 26.5. | Kähler surfaces and symplectic 4-manifolds, constraints on symplectic 4-manifolds | Jonathan Bowden | [D, Kotsch] | Notes |
| 2.6. | Adjunction inequality and Thurston norm detection | Raphael Zentner | [K,KM2] | Recording , Notes |
| 9.6. | Glueing formulae, existence of infinitely many smooth structures | Piotr Suwara | [KM] | Recording , Notes |
| 16.6. | Fibredness detection | Paolo Ghiggini | [G] | Recording , Notes |
| 23.6. | Seiberg-Witten theory for families of 4-manifolds | Piotr Suwara | [R] | Recording , Notes |
| 30.6. | Gauge theory on 4-manifolds with periodic end | Felix Eberhart | [Tau] | Recording , Notes |
| 7.7. | Floer homotopy type and refined Seiberg-Witten invariants | Markus Upmeier | Notes | |
| 14.7. | Donaldson's diagonalisation theorem via Seiberg-Witten theory | Paolo Ghiggini |