Freiburg / Göttingen Seminar
Physical Approach To Donaldson And Seiberg-Witten Invariants Of Four-Manifolds

Day 1: Freiburg, 04.05

Speaker Room
10:15-11:45 Gaussian integral and the supersymmetric localization [M, 3.1, 3.2; H, Ch. 9] Andreas Ikkert SR 218
12:00-13:00 Lunch
13:00-14:30 Mathai-Quillen integral representation of the Thom class [M, 3.3, 3.4], [BT, I.6, II.12] Evgenij Pascual SR 218
15:00-16:45 Equivariant cohomology [M, 3.5], [BGV, Ch.7] (time-permitting [M, 3.6]) Victor Pidstrygach SR 404

Day 2: Göttingen, 11.05

Speaker Room
11:45-13:15 Equivariant cohomology II Victor Pidstrygach H3
13:15-14:15 Lunch
14:15-15:45 Topological twist of N=2 field theories [M, 4.1+4.2] Emanuel Scheidegger H3

Day 3: Freiburg, 12.06

Speaker Room
11:30-13:00 Topological twist of N=2 field theories II Emanuel Scheidegger SR 414
13:00-14:00 Lunch
14:00-15:30 Moduli spaces of Instantons [M, 4.3] Andriy Haydys SR 127
16:00-17:30 Cohomological descent and observables (+ repeat of BRST model) [M, 4.4], [W1, pp. 4-8], [AJ], [CMR, 10.5, 15.5, 15.8.3], [W2] Victor Pidstrygach SR 127

Day 4: Göttingen, 15.06

Speaker Room
12:00-13:45 Observables Victor Pidstrygach H1
13:15-14:15 Lunch
14:15-15:45 Donaldson polynomials [M, 4.5], [DK], [CMR, 15.8] Andriy Haydys / Victor Pidstrygach H1
16:15-17:45 The Donaldson-Witten partition function [M, 4.6], [CMR, 15.8], [W2] Andreas Ikkert Maximum

Special talk: Freiburg, 21.06

Speaker Room
14:15-15:15 Multi-monopole invariants and Vertex Algebras Sergei Gukov SR 414

Day 5: Freiburg, 26.06

Speaker Room
11:30-13:30 Hypermultiplets and monopole equations [M, 4.7], [W3] Evgenij Pascual SR 414
13:30-14:30 Lunch
14:30-16:45 Complex integrable systems and special Kähler geometry Andriy Haydys SR 218
17:15-18:35 Ghosts Victor Pidstrygach SR 404

Day 6: Göttingen, 29.08

Speaker Room
13:15-16:15 Introduction to the u-plane in the Seiberg-Witten SU(2)-theory Murad Alim H1
16:15-17:45 Discussion
Notes* (5.2Mb) of all talks.

Literature

[AJ] Atiyah, Jeffrey. Topological Lagrangians and cohomology.
[BGV] Berline, Getzler, Vergne. Heat Kernels and Dirac Operators.
[BT] Bott, Tu. Differential forms algebraic topology.
[CMR] Cordes, Moore, Ramgoolam. Lectures...
[DK] Donaldson, Kronheimer. Geometry of four-manifolds.
[H] Hori et al. Mirror symmetry.
[M] Moore. Lectures On The Physical Approach To Donaldson And Seiberg-Witten Invariants Of Four-Manifolds. Available online.
[W1] Witten. Introduction to cohomological field theories.
[W2] Witten. Topological Quantum Field Theory.
[W3] Witten. Monopoles and 4-manifolds.

*These notes combine mistakes of the speakers with those of mine; No warranty provided, use at your own risk. If unsure, do not click.