Mihnea Popa,
Spectral Curves and Moduli Spaces of Vector Bundles
The notion of spectral curve was first introduced in the sixties, in
the theory of integrable systems. In the late eighties--beginning with
work of N.Hitchin--it started to be applied very succesfully to problems
related to linear series on moduli spaces of vector bundles on curves.
It basically provides an "abelianization" of the problem, reducing the
above questions to questions about linear series on some Jacobians, which
sometimes are much easier to answer.
This will be a very algebro-geometric talk, providing a basic
introduction to the theory of spectral curves and hints for how they are
used in the moduli problems. Your comments about other applications to
integrable systems or the Langlands program will be highly appreciated.