Mikhail Mikhailovich Kapranov

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Michail Michailowitsch Kapranow , ( Russian Михаил Михайлович Капранов ; English transcription Mikhail Kapranov; * 1962 ) is a Russian mathematician who deals with algebraic geometry , representation theory and mathematical physics .

Kapranov graduated from Lomonosov University in 1982 and received his doctorate in 1988 from Yuri Manin at the Steklow Institute in Moscow. He was then a scientist at the Steklow Institute and from 1990 at Cornell University . In 1991 he was Assistant Professor, 1993 Associate Professor and 1995 Professor at Northwestern University . From 1999 to 2003 he was a professor at the University of Toronto and since 2003 he has been a professor at Yale University . In 1993 he became a Sloan Research Fellow .

With Israel Gelfand he investigated generalizations of hypergeometric functions and their connections with discriminants , which according to them goes back to studies by Arthur Cayley (1848), and hyperdeterminants (generalizations of determinants in multidimensional matrices). In 1995 he formulated a higher-dimensional Langland correspondence . and dealt with higher dimensional category theory .

At the end of the 1980s he worked with Wladimir Wojewodski on -Gruppoide, following an idea by Alexander Grothendieck (Esquisse d'un program). Carlos Simpson found inconsistencies in 1998, and Voevodsky found an explicit mistake in 2013. Kapranow was also involved in the beginning of Voivodski's program to develop a motivic cohomology, but then went his own way.

In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( Operads and Algebraic Geometry ).

Fonts

  • with Israel Gelfand, Andrei Zelevinsky : Discriminants, Resultants and Multidimensional Determinants, Birkhäuser 1994
  • with Ezra Getzler (editor): Higher Category theory, Contemporary Mathematics Vol. 230, 1998, American Mathematical Society
  • Analogies between the Langlands correspondence and topological quantum field theory, in: S. Gindikin, J. Leopowsky, RL Wilson (eds.), Functional analysis at the eve of the 21st century (Gelfand 80th birthday volume), Volume 1, Birkhäuser 1995 , Pp. 119-151

Web links

References and comments

  1. ↑ Michail Michailowitsch Kapranow in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ In the view of Gelfand and co-authors, the discriminants represent a “quantization” of the differential equation of the hypergeometric functions
  3. ↑ Mikhail Kapranov, Analogies between the Langlands correspondence and topological quantum field theory, in Gelfand, Gnidikin, Lepowsky, Wilson (editor): Functional Analysis on the Eve of the 21st Century, (Festschrift on the 80th birthday of Gelfand) Vol. 1, Birkhäuser, 1995, pp. 119–151.
  4. ↑ Wojewodski, The Origins and Motivations of Univalent Foundations, IAS 2014
personal data
SURNAME Kapranow, Michail Michailowitsch
ALTERNATIVE NAMES Kapranov, Mikhail; Капранов, Михаил Михайлович (Russian spelling)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH 1962