**M.S. Raghunathan**

IIT, Mumbai

August 4, 2016

**The Narasimhan-Seshadri Theorem revisited**:
The Narasimhan-Seshadri Theorem characterizes stable bundles on a curve of genus $geq 2$ as bundles obtained from irreducible unitary
representations of suitable Fuchsian groups (acting on the unit disc). In this talk we give a proof of the theorem which is somewhat simpler than that of Narasimhan and Seshadri. The essential strategy of the proof is the same as theirs but we avoid the use made by them of relatively deep results from the Kodaira-Spencer (complex analytic) deformation theory.