Abstract: The Hitchin-Kobayashi correspondence states that the moduli space of stable vector bundles over a projective manifold coincides with the moduli space of Einstein-Hermitian vector bundles. Over the years, this result and its consequences have served as a motivation to relate the existence of metrics of constant curvature on polarized manifolds to an algebraic condition (K-stability). The correspondence between stable and Einstein-Hermitian vector bundles has a well-known generalization in the context of Higgs bundles, where one studies Hitchin's harmonic bundle equations. In this talk we will describe how to give an analogous construction in the category of polarized varieties, thus defining what a "Higgs field" should be in this context and studying a system of equations that naturally arises from the construction.

Note: After the talk we will be discussing the future plans for the seminar.

http://users.ictp.it/~arincon/AGS.html