Martin Ulirsch (Frankfurt) 3 June 2021 "Parabolic Higgs bundles on toric varieties" In this talk I will explain a version of Simpson’s non-abelian Hodge correspondence on a toric variety X. There is a natural 1-1 correspondence between stable parabolic Higgs bundles on X and irreducible representations of the fundamental group of the big torus. This correspondence reduces to a correspondence between toric vector bundles and integral unitary representations in a suitable sense. In this story the spherical Tits building will have a surprise appearance. The main result suggests (at least to me) that there is a yet-to-be-discovered logarithmic incarnation of the non-abelian Hodge correspondence.
