Professor Galicki will continue his research in hyperkahler and quaternionic geometry related to problems in mathematical physics. He will construct new Kahler metrics which are invariant under a quaternionic action on the space and which satisfy prescribed curvature conditions. In addition, Professor Galicki will study certain first order differential systems analogous to the vortex equation and monopole equations. The principal investigator's work is cross disciplinary. The research in the differential geometry of quaternionic manifolds often uses results and methods of mathematical physics. At the same time, the powerful methods of differential geometry frequently bring about a better understanding of important problems in the search for a unified field theory.
