Geometry Forum (special edition)
Tuesday, April 14, 2009, 8:30am, 227 Physics
Graham Cox (Duke University)
The Yang--Mills equations over Riemann surfaces
Abstract:- In this talk I will describe some interactions between the moduli space of
stable holomorphic bundles over a Riemann surface and the space of minimal
unitary Yang-Mills connections, as presented by Atiyah and Bott in their
paper "The Yang-Mills Equations over Riemann Surfaces". The Yang-Mills
energy will be considered as a Morse function on the space of connections,
and its nullity and index computed in terms of the sheaf cohomology of
certain holomorphic bundles. I will also describe how the standard
holonomy correspondence can be extended to relate unitary Yang-Mills
connections (not necessarily flat) to projective unitary representations
of the fundamental group. Finally, a stratification of the moduli space
that occurs in algebraic geometry will be presented. This is precisely
the stratification one would expect from the Yang-Mills functional;
however, the proof that such a Morse stratification even exists would
require rather strong convergence results for the Yang-Mills gradient
flow, and so this correspondence is left at a conjectural level.
Generated at 7:23pm Tuesday, April 16, 2024 by Mcal. Top
* Reload
* Login