Description
Speaker: Sudarshan Gurjar
Title: Introduction to Higgs bundles
Abstract: A Higgs bundle on a compact Kahler manifold M consists of a
holomorphic vector bundle E together with a holomorphic 1-form with values
in End(E), say \phi, such that \phi^\phi = 0 as a 2-form with values in
End(E). It turns out that there is a one to one correspondence between
irreducible representations of fundamental group of M and stable Higgs
bundles on M with vanishing Chern classes. This can be seen as the
analogue of the Narasimhan-Seshadri theorem connecting irreducible unitary
representations of the fundamental group with stable, flat vector bundles.