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Wednesday, October 4, 2017

**Abstract:** The Narasimhan and Seshadri theorem, one of the seminal first results in the study of the moduli space of vector bundles over a Riemann surface, relates degree zero, stable vector bundles on a compact Riemann surface $X$ with unitary representations of ${{\pi }_{1}}\left( X \right)$. One direction to generalize this theorem is by allowing punctures in the Riemann surface and the correspondence, which now involves parabolic bundles, was carried out by Mehta and Seshadri. The version for fundamental group representations of the punctured Riemann surface into Lie groups other than $G=\text{U}\left( n \right)$ entails introducing the notion of parabolic Higgs bundles. We will describe these holomorphic objects and see examples of those corresponding to Fuchsian representations of the fundamental group of the punctured Riemann surface.

Wednesday, October 18, 2017

Wednesday, October 25, 2017

Wednesday, November 8, 2017

Wednesday, November 15, 2017