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The Geometry of Four-Manifolds learning seminar (spring 2026)

Organized by myself and Adrian Flores.
Based loosely on a reading group organized by Qiuyu Ren.
Fridays at 2 pm in PMA 12.166
Mailing list: donkron@utlists.utexas.edu

Schedule

Week 0 (1/16):	Organizational meeting
Week 1 (1/23):	Review of gauge theory (á la Imogen)	John	[DK 2.1,2.2]
Week 2 (1/30):	Review of elliptic PDEs	Justin Toyota	[MS Appendix B]
Week 3 (2/6):	Uhlenbeck's theorem I	Jemma	[DK 2.3]
Week 4 (2/13):	Uhlenbeck's theorem II	Ioannis	[DK 2.3]
Week 5 (2/20):	Yang-Mills moduli spaces (stratification/local models)	Justin Chen	[DK 4.1, 4.2]
Week 6 (2/27):	Transversality	Jemma	[DK 4.3]
Week 7 (3/6):	Compactness	Adrian	[DK 4.4], [Uh], Qiuyu Ren's notes
Week 8 (3/13):	Cohomology of the orbit space of connections	John	[DK 5.1]
Week 9 (3/27):	K-Theory and determinant line bundles	Jake	[DK 5.1,5.2,5.4], [MS Appendix A]
Week 10 (4/3):	Orientation of the moduli space	Adrian	[DK 5.4]
Week 11 (4/10):	Proof of diagonalization	Hyun-soo	[DK 8.1], [Do]
Week 12 (4/17):	Intro to instanton Floer homology/instantons in physics

Sources:

• [DK] S. K. Donaldson and P. B. Kronheimer, The Geometry of Four-Manifolds, Oxford Mathematical Monographs, 1990.
• [MS] McDuff and Salamon, J-holomorphic Curves and Symplectic Topology, AMS Colloquium Publications, Vol. 52, 2012.
• [Uh] Uhlenbeck, Connections with L^p bounds on curvature, Comm. Math. Phys. 83 (1982), no. 1, 31-42.
• [Do] S. K. Donaldson, An application of gauge theory to four-dimensional topology, Journal of Differential Geometry, 18 (2): 279-315, 1983.