The Yang--Mills Equations over Riemann Surfaces

<p><p>

(Based on the paper of Atiyah--Bott of the same title) I'll talk
about two approaches (differential geometric and complex analytic) to the
moduli space of vector bundles over Riemann surfaces.  One important
technique is to study the critical points of the "Yang--Mills" functional
of a connection on a principal G-bundle.  This leads to some understanding
of the topology of the moduli space of vector bundles.