Inculcation: integrable systems, vector bundles, gauge theory, topology of manifolds, geometric representation theory, enumerative geometry, quantum cohomology, TQFTs, Frobenius manifolds, singulatity theory, mirror symmetry

wikipedia Integrable system - Wikipedia
book Olivier Babelon, Denis Bernard, Michel Talon - Introduction to Classical Integrable Systems
notes An Introduction to Gauge Theory and its Applications connects vector bundles, Yang-Mills in 4 dimensions, topology of smooth 4-manifolds, algebraic geometry of stable holomorphic bundles and Hitchin integrable systems
article How to count curves? - Ian Strachan
book Integrable systems twistors, loop groups and Riemann surfaces
lecture notes and problems Integrable systems (Math 99r, Spring 2024) - Sanath Devalapurkar
references Mathematical Retreat on Integrable Systems
references Some recent books on symmetries, integrability and all that (1999-2004)
lecture videos Short course on Hitchin Integrable Systems, 1st lecture. Tom Sutherland (Lisbon University). - YouTube
book E Markman, “Spectral curves and integrable systems”
book J Hurtibuse, “Separating coordinates for the generalized Hitchin systems and the classical r-matrices”
book A Gorsky, N Nekrasov, V Rubtsov, “Hilbert Schemes, Separated Variables, and D-Branes”
talk video A tale of supersymmetry: The dark magic of integrable systems - YouTube with slides following paper Seiberg-Witten integrable systems

wiki https://en.wikipedia.org/wiki/Template:Integrable_systems

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