Bruno Premoselli

We construct new examples of compact, negatively curved Einstein four-manifolds. More precisely, we construct Einstein metrics of
negative sectional curvature on branched covers of suitable compact hyperbolic four-manifolds, initially considered by Gromov and Thurston.
These metrics are obtained through a deformation procedure: our approximate metric is an interpolation between a model Einstein metric near
the branch locus and the pull-back of the hyperbolic metric on the branched cover; we then deform it into a genuine solution to Einstein’s
equations. Our construction yields the first example of compact Einstein manifolds with negative scalar sectional curvature which are not
locally homogeneous. This is a joint work with J. Fine (ULB).