Seminar by Ian McIntosh (University of York)

Title: Using Higgs bundle moduli to get at minimal surface moduli

2016.07.29 | Christine Dilling

Date Wed 14 Sep
Time 15:15 16:15
Location Aud D3


A foundational result in the study of G-Higgs bundles says that for every stable G-Higgs bundle over a compact Riemann surface (of genus at least two) there is a unique equivariant (or "twisted") harmonic map from the (universal cover of the) surface to the non-compact symmetric space N corresponding to G (a non-compact real reductive group). This map is minimal exactly when the Higgs field has vanishing trace-squared: this subvariety of G-Higgs bundles is sometimes called the nilpotent cone. This means it should be possible to parametrise twisted minimal maps using Higgs bundle data. John Loftin (Rutgers) and I have recently done this for the case where G=PU(2,1), whose symmetric space is the complex hyperbolic plane. I will explain how this works, and how this gives some hints about what to expect more generally.