Vladimir Markovic studies the shape and structure of topological spaces known as manifolds. He is an expert in low-dimensional topology — concerning manifolds of fewer than four dimensions — and his world-leading research has particularly improved our understanding of the topology of closed 3-manifolds (three-dimensional manifolds).
Vladimir has solved well-known mathematical problems in hyperbolic geometry, including — together with Jeremy Kahn in 2009 — William Thurston’s conjecture that every closed hyperbolic 3-manifold contains an almost geodesic immersed surface. Building on this, in 2011 they provided the proof of the Ehrenpreis conjecture whilst coining the ‘good pants homology’ as a way to describe the building blocks of hyperbolic surfaces.
These two significant bodies of work were recognised when Vladimir received the Clay Research Award in 2012. He has also been awarded both the London Mathematical Society’s Whitehead Prize and the Leverhulme Trust’s Philip Leverhulme Prize for achievements in his early career.
Professor of Mathematics and Senior Research Fellow, All Souls College, University of Oxford