Speaker
Prof.
Igor Krichever
(Columbia University)
Description
Harmonic maps of two-dimensional Riemann surface $\Sigma$ to a Riemann manifold $M$ are of interest both in physics and mathematics. They are critical points of the Dirichlet functional, the sigma model action.
In the talk a new approach to the study of these models will be presented. In particular we show that the Dubrovin-Krichever-Novikov hierarchy can be seen as a family of commuting symmetries of the $CP^n$ sigma model. As a corollary we prove that the spectral curves associated with harmonic maps of two-torus to spheres are algebraic.
The talk is based on a joint work with Nikita Nekrasov
Primary author
Prof.
Igor Krichever
(Columbia University)
