Physik Sommersemester 2008
06081 Integrable Systems [V]
Dozent Carberry E.
Dauer 2 SWS
Studiensemester 8
Schein Ja (Übungen)
Termin 14:00-15:30, Do
Inhalt Integrable Systems and the Self-Duality Equations

We will begin with a general tour of integrable systems as they appear in geometry, with a number of examples of integrable systems and an explanation of how they relate to Lax equations and symplectic geometry. We will then discuss the seminal work of Hitchin on the moduli space of solutions to the self-duality equations over a Riemann surface.

Begleitend 06083
Literatur Twistors, Loop Groups, and Riemann Surfaces, by Hitchin, Segal, Ward (Hitchin's Chapter);
Linearizing Flows and a Cohomological Interpretation of Lax Equations, by Philipp A. Griffiths - American Journal of Mathematics, Vol. 107, No. 6 (Dec., 1985), pp. 1445-1484;
The self-duality equations on a Riemann surface, Nigel Hitchin, Proc. London Math. Soc. (3) 55 (1987), 59-126. MR 89a32021;
Stable bundles and integrable systems, Nigel Hitchin, Duke Math. J. 54 (1987), 91-114, MR 88i:58068
(The last two will not be studied in full; we will do as much as time permits)

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