# Vladimir Markovic

**Category: **Research Award Winners

**Affiliation: ** Caltech

The 2012 Clay Research Award was made to Jeremy Kahn and Vladimir Markovic for their work in hyperbolic geometry: (1) their proof that a closed hyperbolic three-manifold has an essential immersed hyperbolic Riemann surface, i.e. the map on fundamental groups is injective; (2) their solution of the Ehrenpreis conjecture: that given any two compact hyperbolic Riemann surfaces, there are finite covers of the two surfaces which are arbitrarily closed in the Teichmüller metric.