Proceedings_of Symposia in Pure Mathematics Volume 62.2, 1997 Seiberg-Witten Integrable Systems Ron Y. Donagi Contents Introduction §1. Some physics background Electromagnetism Yang-Mills theory Quantization Supersymmetry N = 2 super Yang-Mills Duality The Seiberg-Witten solution Adding Matter §2. Why integrable systems? Algebraically integrable systems Seiberg-Witten differentials Linearity: complexified Duistermaat-Heckman §3. Which integrable system? Meromorphic Higgs bundles The spectral curves Elliptic solitons Tests Consistency with Seiberg-Witten Mass to zero: the N=4 limit T to oo: the flow to pure N=2 Higgs to oo: symmetry breaking Singularities §4. Other integrable systems Pure N = 2 SYM The Toda system 1991 Mathematics Subject Classification. Primary: 81T13, 81T60, 58F07. Secondary: 14D20, 14H40. Work partially supported by NSF grant DMS95-03249, and by grants from the Univesity of Pennsylvania Research Foundation and The Harmon Duncombe Foundation. © 1997 American Mathematical Society http://dx.doi.org/10.1090/pspum/062.2/1492533

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