Vector bundles over real algebraic curves

The purpose of this talk is to give an introduction to the study of vector bundles over real algebraic curves, using methods of differential geometry (gauge theory and orbifold fundamental groups). I will give an overview of the Narasimhan-Seshadri correspondence in this context and of what is known about the topology of moduli spaces of Real and Quaternionic vector bundles. This talk is partly based on joint work with Melissa Liu.