Abstract: I will survey recent progress on the asymptotic geometry of the Hitchin metric on the moduli space of Higgs bundles. Gravitational instantons are complete 4-dimensional hyperkähler manifolds with square-integrable curvature tensor. I will address the question whether all gravitational instantons (of type ALG) can be obtained as Hitchin moduli spaces. This is all based on joint work with Fredrickson, Mazzeo and Swoboda.
If you are interested in participating online please contact Tobias Weich in order to receive the login details.