Vladimir Markovic

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Jeremy Kahn and Vladimir Markovic (cropped) .jpg

Vladimir Markovic (* 1973 in Germany ) is a Yugoslav-American mathematician. He deals with low-dimensional geometry and topology ( hyperbolic geometry ) and Riemann surfaces (Teichmüller theory).

Markovic studied from 1992 at the University of Belgrade , where he completed his diploma in 1995 and received his doctorate under Miodrag Mateljevic in 1998 ( clearly extremal, quasi- conformal images and stationary points on the energy integral , Yugoslavian). From 1998 to 2000 he was Assistant Professor at the University of Minnesota and from 2001 Lecturer , from 2004 Reader and from 2006 to 2011 Professor at the University of Warwick . From 2006 to 2008 he was also an Associate Professor at the State University of New York at Stony Brook . He has been a professor at Caltech since 2011 , currently on leave. In 2012 he was visiting professor at the Institut Henri Poincaré . He is currently the Sadleirian Professor of Pure Mathematics at Cambridge University .

In 2002 he received an EPSRC Advanced Research Fellowship Award, in 2004 the Whitehead Prize and in 2004 the Leverhulme Prize. In 2012 he and Jeremy Kahn received the Clay Research Award for work in hyperbolic geometry : their proof that there is an immersed , -injective , closed surface in every closed hyperbolic 3-manifold , and their proof of the honorary award presumption . This means that for two compact hyperbolic Riemannian surfaces there exist finite superpositions which are arbitrarily close with regard to the Teichmüller metric . In 2013 he proved the Schoen conjecture .

In 2014 he was elected to the Royal Society , which in the same year honored him with a Wolfson Research Merit Award . In 2014 he was invited speaker at the ICM in Seoul ( The surface subgroup and the Ehrenepreis Conjectures ).

Fonts

  • Harmonic maps between 3-dimensional hyperbolic spaces. Invent. Math. 199 (2015), no.3, 921-951.
  • with J. Kahn: Immersing almost geodesic surfaces in a closed hyperbolic three manifold. Ann. of Math. (2) 175 (2012), no. 3, 1127-1190.
  • with A. Marden , DBA Epstein : Quasiconformal homeomorphisms and the convex hull boundary. Ann. of Math. (2) 159 (2004) no. 1, 305-336.
  • with A. Fletcher: Quasiconformal maps and Teichmüller Theory. Oxford University Press, 2007.
  • with Y. Komori, Caroline Series : Kleinian Groups and Hyperbolic 3-Manifolds. London Mathematical Society Lecture Notes 299, Cambridge University Press, 2002.
  • with A. Fletcher: Infinite dimensional Teichmüller Spaces. In: Handbook of Teichmüller Theory. Volume 2, European Mathematical Society, 2009, pp. 65-91.
  • Harmonic maps between 3-dimensional hyperbolic spaces , Invent. Math., Volume 199, 2015, pp. 921-951.
  • Harmonic maps and the beautiful conjecture , J. Amer. Math. Soc., Volume 30, 2017, pp. 799-817.

Web links

Individual evidence

  1. ↑ This means that there is a continuous (not necessarily injective) mapping from the surface into the 3-manifold, so that the mapping induced by this between the respective fundamental groups is injective, see also incompressible surface . Kahn, Markovic: Immersing almost geodesic surfaces in a closed hyperbolic 3-manifold. Preprint 2009, 2011 , appears in Annals of Mathematics
  2. ^ Kahn, Markovic: The good pants homology and a proof of the Ehrenpreis conjecture. Preprint 2011.
  3. ^ Clay Research Award. ( Memento from November 3, 2013 in the Internet Archive )
  4. ^ Royal Society announces new round of esteemed Wolfson Research Merit Awards. At: royalsociety.org. May 9, 2014, accessed March 2, 2015.
personal data
SURNAME Markovic, Vladimir
BRIEF DESCRIPTION Yugoslav-American mathematician
DATE OF BIRTH 1973
PLACE OF BIRTH Germany