Vladimir Turaev
{{Short description|Russian mathematician (born 1954)}}
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 his Candidate of Sciences degree (PhD) under Oleg Viro.{{MathGenealogy|id=56929}} Turaev was a professor at the University of Strasbourg and then became a professor at Indiana University. In 2016, he was elected a Fellow of the American Mathematical Society.
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;{{cite journal|author=Reshetikhin, N.|author2=Turaev, V. G.|title=Invariants of 3-manifolds via link polynomials and quantum groups|journal=Inventiones Mathematicae|volume=103|issue=3|year=1991|pages=547–597|doi=10.1007/BF01239527|url=http://eudml.org/doc/143870|bibcode=1991InMat.103..547R|s2cid=123376541|url-access=subscription}} 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;{{cite journal|author=Turaev, V. G.|author2=Viro, O. Y.|title=State sum invariants of 3-manifolds and quantum 6j-symbols|journal=Topology|volume=31|issue=4|year=1992|pages=865–902|doi=10.1016/0040-9383(92)90015-A|doi-access=}} 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.{{cite book|author=Turaev, Vladimir G.|chapter=State sum models in low-dimensional topology|title=Proc. ICM Kyoto|volume=1|pages=689–698|year=1990|chapter-url=https://www.researchgate.net/publication/265451900}} 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=
- {{cite journal|title=The Yang-Baxter equation and invariants of links|journal=Inventiones Mathematicae|volume=92|issue=3|year=1988|pages=527–553|doi=10.1007/BF01393746|last1=Turaev|first1=V. G.|bibcode=1988InMat..92..527T|s2cid=122703873}}
- with Nicolai Reshetikhin: {{cite journal|doi=10.1007/BF02096491|title=Ribbon graphs and their invariants derived from quantum groups|journal=Communications in Mathematical Physics|volume=127|issue=1|year=1990|pages=1–26|last1=Reshetikhin|first1=N. Y.|last2=Turaev|first2=V. G.|bibcode=1990CMaPh.127....1R|s2cid=122572484}}
- {{cite journal|url=https://eudml.org/doc/82308|title=Skein quantization of Poisson algebras of loops on surfaces|journal=Annales Scientifiques de l'École Normale Supérieure|volume=24|issue=6|pages=635–704|year=1991|doi=10.24033/asens.1639|last1=Turaev|first1=Vladimir G.|doi-access=free}}
=Books=
- Quantum invariants of Knots and 3-Manifolds, de Gruyter 1994;{{cite journal|title=Review of Quantum invariants of knots and 3-manifolds by V. G. Turaev|author=Kuperberg, Greg|authorlink=Greg Kuperberg|journal=Bull. Amer. Math. Soc.|volume=33|year=1996|pages=107–110|doi=10.1090/S0273-0979-96-00621-0|doi-access=free}} {{cite book|title=2nd edition|year=2010}};{{cite web|author=Taylor, Scott|date=10 June 2011|url=https://www.maa.org/press/maa-reviews/quantum-invariants-of-knots-and-3-manifolds|website=MAA Reviews, Mathematical Association of America|title=Review of Quantum Invariants of Knots and 3-Manifolds by Vladimir G. Turaev}} {{cite book|title=3rd edition|year=2016|url=https://books.google.com/books?id=6bqvDAAAQBAJ|isbn=9783110435221|last1=Turaev|first1=Vladimir G.|publisher=Walter de Gruyter GmbH & Co KG }}
- with Christian Kassel and Marc Rosso: Quantum groups and knot invariants, SMF (Panoramas et Synthèses) 1997
- as editor with Anatoly Vershik: [https://books.google.com/books/about/Topology_Ergodic_Theory_Real_Algebraic_G.html?id=W_BqjwEACAAJ Topology, ergodic theory, real algebraic geometry - Rokhlin´s memorial], American Mathematical Society 2001
- [https://books.google.com/books/about/Introduction_to_Combinatorial_Torsions.html?id=TcbzBwAAQBAJ Introduction to combinatorial torsions], Birkhäuser 2001
- [https://books.google.com/books/about/Torsions_of_3_dimensional_Manifolds.html?id=83ZJs9Z9BY0C Torsions of 3-dimensional manifolds], Birkhäuser 2002
- with Christian Kassel: [https://books.google.com/books?id=kwa3yIKVTdwC Braid Groups], Springer 2008, {{ISBN|0-387-33841-1}}{{cite journal|title=Review of 2 books: Braid groups by Christian Kassel and Vladimir Turaev (with the graphical assistance of Olivier Douane); Ordering braids by Patrick Dehornoy|author=Birman, Joan S.|authorlink=Joan Birman|journal=Bull. Amer. Math. Soc.|volume=48|year=2011|pages=137–146|doi=10.1090/S0273-0979-2010-01305-7|doi-access=free}}{{cite web|title=Review of Braid Groups by Christian Kassel and Vladimir Turaev|author=Taylor, Scott|date=13 October 2011|website=MAA Reviews, Mathematical Association of America|url=https://www.maa.org/publications/maa-reviews/braid-groups}}
- [https://books.google.com/books/about/Homotopy_Quantum_Field_Theory.html?id=v4hty8W-guAC Homotopy quantum field theory], European Mathematical Society 2010{{cite journal|title=Review of Homotopy quantum field theory by Vladimir Turaev|author=Porter, Timothy|journal=Bull. Amer. Math. Soc.|volume=49|issue=2|year=2012|pages=337–345|doi=10.1090/S0273-0979-2011-01351-9|doi-access=free}}
- with Alexis Virelizier: [https://books.google.com/books/about/Monoidal_Categories_and_Topological_Fiel.html?id=sjUqDwAAQBAJ Monoidal Categories and Topological Field Theory], Birkhäuser 2015
See also
References
{{reflist}}
External links
- [https://math.indiana.edu/about/faculty/touraev-vladimir.html Vladimir Touraev, Mathematics Department, Indiana University]
- [http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=21914 mathnet.ru]
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Category:20th-century Russian mathematicians
Category:21st-century Russian mathematicians
Category:Fellows of the American Mathematical Society
Category:Academic staff of the University of Strasbourg