Topics in Symplectic Geometry (2018 Fall)

• Room: ºî¤T734
• Time: Wednesday 567
• Office Hour: By appointment

Course Description

• Yang-Mills theory and moduli spaces of flat connections
• Hitchin's equations and their moduli spaces
• Representation varieties and Quasi-Hamiltonian system

References (with be updated throughout the course)

• L. Jeffrey, Hamiltonian Group Actions and Symplectic Reduction, IAS/Park City Mathematics Series
• A. Silva, Lectures on Symplectic Geometry, LNM 1764, Springer
• L. Duistermaat and J. Kolk, Lie groups (1.1-1.4: Lie group and Lie algebra; 2.1-2.4: group actions and associate bundles), UTX, Springer
• Theodor Br\"{o}cker and Tammo tom Dieck, Representations of Compact Lie Groups, GTM 98, Springer

• M. Atiyah, The Geometry and Physics of Knots

• V. Guillemin and S. Sternberg, Symplectic techniques in Physics (III. Motion in a Yang-Mills field)
• J. Jost, Riemannian Geometry and Geometric analysis (3, 4.1-4.2), UTX, Springer
• K. Donaldson, The Geometry of four manifolds, (Chapter 2,4,6)

• S. Kobayashi, Foundations of Differential Geometry I & II
• C. Taubes, Differential Geometry: Bundles, connections, metrics and curvature

• W.M. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math. (1984).
• A. Alekseev, A. Malkin, and E. Meinrenken, Lie group valued moment maps, J. Differential Geom. (1998)

• Atiyah and Bott, The Yang-Mills equations over Riemann surfaces,Philos. Trans. Roy. Soc. London Ser. A (1983)
• M. Atiyah, Collected works, Volume 5 - Gauge theories
• N. Hitchin, Self-duality equations on a Riemann surface, Proc. London Math. Soc. (1987)
• W.M. Goldman and J.J. Millson, The deformation theory of representations of fundamental groups of compact K\"{a}hler manifolds, Bull. Amer. Math. Soc. (N.S.) (1988),

Evaluation

• One Exam