**ODTU-B****I****LKENT
ALGEBRAIC GEOMETRY SEM****I****NAR**

**“Introduction to spectral curves”**

by

**AlI
ULAS OZGUR KISISEL**

**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.**