Alexander Resnikov

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Alexander G. Resnikow ( Russian Александр Резников ; English transcription Alexander Reznikov; born January 14, 1960 in Kiev ; † September 5, 2003 ) was a Russian mathematician who studied geometry (Riemannian geometry, symplectic geometry, geometric group theory, topology of three-dimensional Manifolds, algebraic geometry) and dynamical systems.

Life

Reznikov won second prize in the International Mathematical Olympiad in 1975 and began studying at Kiev University in the same year . However, since he was Jewish, he could not do his doctorate at the university straight away and worked at a state planning institute while he was working on his doctorate with Myroslav Gorbachuk in Kiev. Since he had joined a private study group on the history of Israel, he had to leave Kiev and hired himself out as a worker in various parts of the former Soviet Union such as Tajikistan, Lithuania. In 1989 he emigrated to Israel , where he received his doctorate in 1990 with Vitali Milman at Tel Aviv University . After a year as a post-doc at the ICTP in Trieste , he became a lecturer at the Hebrew University in Jerusalem . In 1997 he became Professor of Mathematics at the University of Durham .

In 2000 he was invited speaker at the European Congress of Mathematicians in Barcelona ( Analytic topology ). In 1999 he became a member of the London Mathematical Society .

plant

Reznikov first dealt with differential geometry , in which he proved the weak Blaschke conjecture, which asks whether spheres and projective spaces are the only Blaschke manifolds over the real division algebras (real and complex numbers, quaternions, Cayley numbers). Reznikov proved that all Blaschke manifolds must have the same volume as the example spaces mentioned above. From the 1990s he also dealt with the Haken - Waldhausen - Thurston conjecture, which states that every irreducible 3-manifold with an infinite fundamental group has a finite cover with a positive first Betti number , that is, it is a virtual hook manifold . He proved several theorems about manifolds that are not virtual hook manifolds . He also showed connections between the topology of 3-manifolds and number theory.

Reznikov was best known for proving the Bloch conjecture on the representations of the fundamental group of algebraic varieties .

literature

  • Mikhail Kapranov , Sergiy Kolyada, Yuri I. Manin , Pieter Moree, Leonid A. Potyagailo (Eds.): Geometry and Dynamics of Groups and Spaces. In Memory of Alexander Reznikov (= Progress in Mathematics. 265). Birkhäuser, Basel et al. 2008, ISBN 978-3-7643-8607-8 .
  • Reznikov, Norbert Schappacher (editor): Regulators in analysis, geometry and number theory (= Progress in Mathematics. 171). Birkhäuser, Boston MA et al. 2000, ISBN 0-8176-4115-7 .

Fonts (selection)

Individual evidence

  1. ↑ page at MathNet
  2. ↑ Milman on his Reznikov website
  3. ↑ Reznikov Blaschke Manifolds of projective plane type , Functional Analysis and Applications, Vol. 19, 1985, p. 156
  4. ↑ These are those where the geodesics emanating from this point intersect other geodesics from this point at the same distance (the intersection of the geodesics from each point is a sphere). Blaschke was motivated by the problem of waves propagating on the earth's surface and assumed that waves emanating from any point only meet again at one point on spherical surfaces. McKay The Blaschke Conjecture ( Memento from July 13, 2012 in the web archive archive.today ). His original problem (for two dimensions) from his lectures on differential geometry was solved by Leon Green in 1963 after Blaschke had in the meantime included an incorrect proof from Kurt Reidemeister in the second edition of his lectures.
  5. ^ Reznikov All regulators of flat bundles are torsion. In: Annals of Mathematics. Series 2, Vol. 141, No. 2, 1995, pp. 373-386. Treated in Christophe Soulé Classes caractéristiques secondaires des fibers plats , Seminaire Bourbaki, No. 819, 1995/1996, online
personal data
SURNAME Resnikov, Alexander
ALTERNATIVE NAMES Resnikow, Alexander G .; Резников, Александр (Russian)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH January 14, 1960
PLACE OF BIRTH Kiev
DATE OF DEATH September 5, 2003