Hartmut Weiss (Kiel) will speak in the geometry seminar at 2pm on 2nd March in the Salle des Profs (9th floor, building NO). Harmut’s title is “Transgressive harmonic maps and SU(1,1)-self-duality solutions” and his abstract is below.
I will report on recent joint work with Sebastian Heller and Lothar Schiemanowski where we describe a duality between equivariant harmonic maps from a Riemann surface to hyperbolic-3-space and to de-Sitter-3-space respectively. This corresponds on the gauge theory side to a duality between SU(2)- and SU(1,1)-solutions of Hitchins’s self-duality equations via a signature flip along an eigenline of the Higgs field. On the SU(2) side it extends to a class of singular solutions which produce transgressive harmonic maps to the 3-sphere, i.e. harmonics maps which pass through the sphere at infinity to a second copy of hyperbolic-3-space attached to the boundary. We construct large energy examples by gluing. If time permits I will sketch an application to the construction of real holomorphic sections of the Deligne-Hitchin moduli space.