Vladimir Turaev
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.[1] 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;[2] 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;[3] 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.[4] In 2016, he shared, with Alexis Virelizier, the Ferran Sunyer i Balaguer Prize for their monograph Monoidal categories and topological field theory.
Selected publications[edit]
Articles[edit]
- Turaev, V. G. (1988). "The Yang-Baxter equation and invariants of links". Inventiones Mathematicae. 92 (3): 527–553. Bibcode:1988InMat..92..527T. doi:10.1007/BF01393746. S2CID 122703873.
- with Nicolai Reshetikhin: Reshetikhin, N. Y.; Turaev, V. G. (1990). "Ribbon graphs and their invariants derived from quantum groups". Communications in Mathematical Physics. 127 (1): 1–26. Bibcode:1990CMaPh.127....1R. doi:10.1007/BF02096491. S2CID 122572484.
- Turaev, Vladimir G. (1991). "Skein quantization of Poisson algebras of loops on surfaces". Annales Scientifiques de l'École Normale Supérieure. 24 (6): 635–704. doi:10.24033/asens.1639.
Books[edit]
- Quantum invariants of Knots and 3-Manifolds, de Gruyter 1994;[5] 2nd edition. 2010.;[6] Turaev, Vladimir G. (2016). 3rd edition. Walter de Gruyter GmbH & Co KG. ISBN 9783110435221.
- with Christian Kassel and Marc Rosso: Quantum groups and knot invariants, SMF (Panoramas et Synthèses) 1997
- as editor with Anatoly Vershik: Topology, ergodic theory, real algebraic geometry - Rokhlin´s memorial, American Mathematical Society 2001
- Introduction to combinatorial torsions, Birkhäuser 2001
- Torsions of 3-dimensional manifolds, Birkhäuser 2002
- with Christian Kassel: Braid Groups, Springer 2008, ISBN 0-387-33841-1[7][8]
- Homotopy quantum field theory, European Mathematical Society 2010[9]
- with Alexis Virelizier: Monoidal Categories and Topological Field Theory, Birkhäuser 2015
See also[edit]
References[edit]
- ^ Vladimir Turaev at the Mathematics Genealogy Project
- ^ Reshetikhin, N.; Turaev, V. G. (1991). "Invariants of 3-manifolds via link polynomials and quantum groups". Inventiones Mathematicae. 103 (3): 547–597. Bibcode:1991InMat.103..547R. doi:10.1007/BF01239527. S2CID 123376541.
- ^ Turaev, V. G.; Viro, O. Y. (1992). "State sum invariants of 3-manifolds and quantum 6j-symbols". Topology. 31 (4): 865–902. doi:10.1016/0040-9383(92)90015-A.
- ^ Turaev, Vladimir G. (1990). "State sum models in low-dimensional topology". In: Proc. ICM Kyoto. Vol. 1. pp. 689–698.
- ^ Kuperberg, Greg (1996). "Review of Quantum invariants of knots and 3-manifolds by V. G. Turaev". Bull. Amer. Math. Soc. 33: 107–110. doi:10.1090/S0273-0979-96-00621-0.
- ^ Taylor, Scott (10 June 2011). "Review of Quantum Invariants of Knots and 3-Manifolds by Vladimir G. Turaev". MAA Reviews, Mathematical Association of America.
- ^ Birman, Joan S. (2011). "Review of 2 books: Braid groups by Christian Kassel and Vladimir Turaev (with the graphical assistance of Olivier Douane); Ordering braids by Patrick Dehornoy". Bull. Amer. Math. Soc. 48: 137–146. doi:10.1090/S0273-0979-2010-01305-7.
- ^ Taylor, Scott (13 October 2011). "Review of Braid Groups by Christian Kassel and Vladimir Turaev". MAA Reviews, Mathematical Association of America.
- ^ Porter, Timothy (2012). "Review of Homotopy quantum field theory by Vladimir Turaev". Bull. Amer. Math. Soc. 49 (2): 337–345. doi:10.1090/S0273-0979-2011-01351-9.
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