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

Articles

• 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

• 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

• Reshetikhin–Turaev invariant