Research Areas

Geometry and Topology

Education

1995-1998 PhD, University of Belgrade

1992-1995 Bachelor, University of Belgrade

Research experience

2024-present Professor, YAU Mathematical Science Center, Tsinghua University

2020-2025 Professor, University of Oxford

2011-2020 John D. MacArthur Professor, CalTech

2013-2014 Sadleirian Professor, University of Cambridge

2000-2011 Professor, University of Warwick

2006-2008 Associate Professor (with tenure), Stony Brook

1998-2000 "Duchnam Jackson" Assistant Professor, University of Minnesota

Honors and rewards

2016 Simons Investigator Award

2014 ICM Invited Speaker, Geometry Section and Dynamical Systems Section, Korea

2014 Elected Fellow of the Royal Society

2014 Research Merit Award, Royal Society

2012 Clay Research Award, awarded by Clay Institute

2004 Whitehead Prize, awarded by LMS

2004 Leverhulme Prize, awarded by Leverhulme Trust

Publications

(1) Homogenization of random quasiconformal mappings and random Delauney triangulations Journal of Differential Geometry 124 (2023), no. 3, 523–551 (with O. Ivrii)

(2) Non-uniqueness of minimal surfaces in a product of closed Riemann surfaces. GAFA, 32, 31–52, (2022)

(3) Caratheodory's Metrics on Teichmueller Spaces and L-shaped pillowcases. Duke Journal of Mathematics 167 (2018), no. 3, 497-535

(4) Harmonic Maps and the Schoen Conjecture. JAMS 30 (2017), no. 3, 799-817

(5) Heat Flows On Hyperbolic Spaces. Journal of Differential Geometry 108 (2018), no. 3, 495-529 (with M. Lemm)

(6) Homology of curves and surfaces in closed hyperbolic 3-manifolds. Duke Journal of Mathematics 164 (2015), no. 14, 2723-2808 (with Y. Liu)

(7) The good pants homology and a proof of the Ehrenpreis conjecture. Annals of Mathematics (2) 182, No. 1, 1-72 (2015) (with J. Kahn)

(8) The moduli space of Riemann surfaces of large genus. GAFA 23 (2013), no. 3, 867-887. (with A. Fletcher and J. Kahn)

(9) Harmonic maps between hyperbolic 3-spaces. Inventiones Mathematicae. 199, No. 3, 921-951 (2015)

(10) Criterion for Cannon's Conjecture. GAFA 23, No. 3, 1035-1061 (2013)

(11) Immersing almost geodesic surfaces in a closed hyperbolic 3-manifold. Annals of Mathematics (2) 175 (2012), no. 3, 1127–1190. (with J. Kahn)

(12) Counting essential surfaces in a closed hyperbolic three-manifold. Geometry and Topology 16 (2012), no. 1, 601–624. (with J. Kahn)

(13) Realization of the Mapping class group by homeomorphisms. Inventiones Mathematicae 168, no. 3, 523–566. (2007)

(14) Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disc. Geometry and Topology 11, 517–595. (2007) (with D. Epstein)

(15) Quasiconformal Maps and Teichm¨uller Theory. Oxford Graduate Texts in Mathematics Oxford University Press (2007) (with A. Fletcher)

(16) Quasisymmetric groups. JAMS 19, no. 3, 673–715 (2006)

(17) Classification of continuously transitive circle groups. Geometry and Topology 10, 1319–1346 (2006) (with J. Giblin)

(18) The logarithmic spiral: A counterexample to the K=2 conjecture. Annals of Mathematics 161, no. 2, 925–957 (2005) (with D. Epstein)

(19) Complex earthquakes and deformations of the unit disc. Journal of Differential Geometry 73, no. 1, 119–166 (2006) (with D. Epstein, A. Marden)

(20) Quasiconformal homeomorphisms and the convex hull boundary. Annals of Mathematics 159, no. 1, 305–336 (2004) (with D. Epstein, A. Marden)

(21) Isometries Between the Spaces of L 1 Holomorphic Quadratic Differentials on Riemann Surfaces of Finite Type. Duke Mathematical Journal 120, no. 2, 433–440 (2003) (with C. Earle)

(22) Biholomorphic maps between Teichm¨uller spaces. Duke Mathematical Journal 120, no. 2, 405–431 (2003)