Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Vladimir Markovic

The 2012 Clay Research Award was made to Jeremy Khan 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.