Mikhail Khovanov

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Mikhail Khovanov ( Russian Михаил Гелиевич Хованов , German  Michail Gelijewitsch Chowanow ; born January 13, 1972 ) is a Russian-American mathematician who deals with representation theory , algebraic topology and knot theory.

Life

Khovanov studied at Lomonosov University , where he graduated in 1991. He received his doctorate in 1997 with Igor Frenkel at Yale University ( Graphical calculus, canonical bases and Kazhdan-Lusztig theory ). As a post-doctoral student , he spent two years at the Institute for Advanced Study and then at the University of California, Davis . He is a professor at Columbia University .

In the late 1990s (at that time he was at the University of California at Davis) he introduced the Khovanov homology of links into knot theory, a new knot invariant obtained by categorizing the Jones polynomial . While this was defined for three dimensions and here, according to Edward Witten, has an interpretation through a topological quantum field theory ( Chern-Simons theory ), the Khovanov homology can be interpreted in four dimensions through topological quantum field theories. Khovanov homology is one of the most successful examples of the categorization process. They are related to the representation theory of Lie algebra and were extended to the corresponding cases by Khovanov and Lev Rozansky (Khovanov-Rozansky homology).

In 2006 he was invited speaker at the International Congress of Mathematicians in Madrid ( Link homology and categorification ).

His half-sister Tanya Khovanova is a mathematician at the Massachusetts Institute of Technology .

Web links

Individual evidence

  1. ↑ In his short portrait at the Univ. California at Davis is described as an undergraduate degree.
  2. ↑ Mikhail Khovanov in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / name used
  3. ↑ Khovanov A categorification of the Jones polynomial , Duke Mathematical Journal, Volume 101, 2000, pp. 359-426, Arxiv
  4. ↑ Khovanov homology in the Knot Atlas, with photo by Khovanov
  5. ↑ Dror Bar-Natan On Khovanov's categorification of the Jones polynomial , Preprint
  6. ↑ Khovanov Homology , entry in the nLab . (English)
  7. ↑ Baez, Dolan Categorification , 1998
  8. ^ Arxiv Preprint
personal data
SURNAME Khovanov, Mikhail
ALTERNATIVE NAMES Хованов, Михаил Гелиевич (Russian)
BRIEF DESCRIPTION Russian-American mathematician
DATE OF BIRTH January 13, 1972