The scope is very wide and involves studying the existence and moduli of solutions to the Euclidean signature Einstein equation as well as the gradient Ricci soliton equation for manifolds on which a compact Lie group acts with cohomogeneity one or which are the total spaces of fibre bundles.
Impact
We succeeded in constructing examples of gradient Kahler Ricci solitons as well as steady and expanding gradient Ricci solitons which are non-Kahlerian. This increased the known examples of such objects in the literature greatly. Complete Ricci flat and negative Einstein structures were also constructed. Worthy of note is that the new examples included ones which are homeomorphic but not diffeomorphic, and their asymptotics included mixed cigar and Bryant type. These are the first such examples.
Student Experience
Undergraduates and masters students were involved in obtaining numerical solutions to the equations under study. A doctoral student is working on a sub-project.
