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Center for Nonlinear Studies |
Since the 70's, algebraic geometry has become one of the most powerful tool in the theory of integrable soliton equations. Explicit periodic or quasi-periodic solutions of the soliton equations are expressed in terms of the Riemann theta-functions corresponding to the auxiliary algebraic curve. The universal Whitham hierarchy is at the core of the perturbation theory of such solutions. Its applications include the theory of topological quantum filed theories, Witten-Seiberg solutions of N=2 supersymmetric gauge theories, and the classical theory of conformal maps. In this talk, basic ideas of the Whitham theory and its most recent applications will be discussed.
Host: Razvan Teodorescu, CNLS/T-13