Vladimir Georgievich Turaev (Владимир Георгиевич Тураев, born in 1954) is a Russian mathematician, specializing in topology.
Turaev received in 1979 from the
Steklov Institute of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part ...
his Candidate of Sciences degree (PhD) under
Oleg Viro
Oleg Yanovich Viro (russian: Олег Янович Виро) (b. 13 May 1948, Leningrad, USSR) is a Russian mathematician in the fields of topology and algebraic geometry, most notably real algebraic geometry, tropical geometry and knot theory.
Co ...
. Turaev was a professor at the
University of Strasbourg
The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers.
The French university traces its history to the ea ...
and then became a professor at
Indiana University
Indiana University (IU) is a system of public universities in the U.S. state of Indiana.
Campuses
Indiana University has two core campuses, five regional campuses, and two regional centers under the administration of IUPUI.
*Indiana Universit ...
. In 2016 he was elected a Fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
Turaev's research deals with low-dimensional topology, quantum topology, and knot theory and their interconnections with quantum field theory. In 1991
Reshetikhin and Turaev published a mathematical construction of new topological invariants of compact oriented 3-manifolds and framed links in these manifolds, corresponding to a mathematical implementation of ideas in quantum field theory published by
Witten
Witten () is a city with almost 100,000 inhabitants in the Ennepe-Ruhr-Kreis (district) in North Rhine-Westphalia, Germany.
Geography
Witten is situated in the Ruhr valley, in the southern Ruhr area.
Bordering municipalities
* Bochum
* Dortmu ...
; the invariants are now called Witten-Reshetikhin-Turaev (or Reshetikhin-Turaev) invariants. In 1992 Turaev and Viro introduced a new family of invariants for 3-manifolds by using state sums computed on triangulations of manifolds; these invariants are now called Turaev-Viro invariants.
In 1990 Turaev was an Invited Speaker with talk ''State sum models in low dimensional topology'' at the
ICM in
Kyōto
Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the ci ...
. In 2016 he shared, with Alexis Virelizier, the Ferran Sunyer i Balaguer Prize for their monograph ''Monoidal categories and topological field theory''.
Selected publications
Articles
*
*with Nicolai Reshetikhin:
*
Books
*''Quantum invariants of Knots and 3-Manifolds'', de Gruyter 1994; ;
*with Christian Kassel and Marc Rosso: ''Quantum groups and knot invariants'', SMF (Panoramas et Synthèses) 1997
*as editor with
Anatoly Vershik
Anatoly Moiseevich Vershik (russian: Анато́лий Моисе́евич Ве́ршик; born on 28 December 1933 in Leningrad) is a Soviet and Russian mathematician. He is most famous for his joint work with Sergei V. Kerov on representati ...
''Topology, ergodic theory, real algebraic geometry - Rokhlin´s memorial'' American Mathematical Society 2001
Birkhäuser 2001
Birkhäuser 2002
*with Christian Kassel
''Braid Groups'' Springer 2008,
European Mathematical Society 2010
*with Alexis Virelizier
Birkhäuser 2015
See also
*
Reshetikhin–Turaev invariant
In the mathematical field of quantum topology, the Reshetikhin–Turaev invariants (RT-invariants) are a family of quantum invariants of framed links.
Such invariants of framed links also give rise to invariants of 3-manifolds via the Dehn surgery ...
References
External links
Vladimir Touraev, Mathematics Department, Indiana Universitymathnet.ru
{{DEFAULTSORT:Turaev, Vladimir
20th-century Russian mathematicians
21st-century Russian mathematicians
Fellows of the American Mathematical Society
University of Strasbourg faculty
Indiana University faculty
1954 births
Living people