“Introduction to spectral curves”








Abstract: The application of tools from algebraic geometry to integrable systems dates back to the 19th century, at least to Jacobi, who found parameterizations of geodesics on an ellipsoid using hyperelliptic theta-functions. In the 20th century, solutions coming from algebraic geometry were found for many equations of mathematical physics, including the KdV, KP, Toda and nonlinear Schrodinger equations. There are also some important cases in which integrable systems played a central role in the solution of a problem which can be purely stated in differential or algebraic geometry. These include the Schottky problem asking for a characterization of Jacobians among all Abelian varieties, classification of harmonic maps from a Riemann surface to a Lie group, or several problems in Gromov-Witten theory and mirror symmetry. My aim in this talk will be to state some of these results after giving some essential definitions, and to underline the place of spectral curves in this picture.








Date:  22 February 2008 Friday
Time: 15:40
Place: Bilkent, Mathematics Seminar Room SA-141


Tea and cookies will be served before the talk.