Moduli spaces of stable Higgs bundles are present in several different mathematical contexts: on the one hand, as generalizations of holomorphic vector bundles these are complex geometric objects. On the other hand, there are close relations to both the fields of geometric analysis and differential topology where – due to foundational results of Hitchin, Simpson, Donaldson, Corlette and others – they appear as solution spaces of nonlinear elliptic PDEs as well as representations of surface groups. In my talk I will highlight some of the resulting rich geometric structures. I will finally present a number of recent results concerning the asymptotic geometry of these moduli spaces and give a glimpse of some currently open problems.
Donnerstag, den 14. November 2019 um 17.15 Uhr, in INF 205, HS, Mathematikon Donnerstag, den 14. November 2019 at 17.15, in INF 205, HS, Mathematikon
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. J. Walcher