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Bertrand Toën

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Bertrand Toën (born September 17, 1973 in Millau, France) is a mathematician who works as a director of research at the Centre national de la recherche scientifique (CNRS) at the Paul Sabatier University, Toulouse, France. He received his PhD in 1999 from the Paul Sabatier University, where he was supervised by Carlos Simpson.

Toën is a specialist of algebraic geometry. He his best known for his systematic use of homotopical methods in algebraic geometry. Together with Gabriele Vezzosi and Jacob Lurie he has laid the foundations of the subject of derived algebraic geometry[1][2][3] and higher category theory.[4][5][6][7][8] His works establish several contributions to noncommutative algebraic geometry in the sense of Kontsevich[9][4] and (shifted) symplectic geometry.[10][11]

He was an invited speaker at the International Congress of Mathematicians in 2014, speaking in the section on "Algebraic and Complex Geometry"[12] with a talk "Derived Algebraic Geometry and Deformation Quantization".[13]


References

  1. ^ B. Toën, G. Vezzosi, Homotopical Algebraic Geometry II: geometric stacks and applications. Mem. Amer. Math. Soc. 193 (2008), no. 902, x+224 pp.
  2. ^ B. Toën, Descente fidèlement plate pour les n-champs d’Artin. Compos. Math. 147 (2011), no. 5, 1382-1412.
  3. ^ G. Vezzosi, What is.... a derived stack? (PDF)
  4. ^ a b B. Toën, The homotopy theory of dg-categories and derived Morita theory. Invent. Math. 167 (2007), no. 3, 615-667.
  5. ^ B. Toën, Vers une axiomatisation de la théorie des catégories supérieures. K-Theory 34 (2005), no. 3, 233-263.
  6. ^ B. Toën, Homotopical and Higher Categorical Structures in Algebraic Geometry. Habilitation thesis, May 2003.
  7. ^ B. Toën, Dualité de Tannaka supérieure. MPI preprint, June 2000
  8. ^ Lurie, Jacob (2009), Higher Topos Theory, Annals of Mathematics Studies, vol. 170, Princeton University Press, arXiv:math.CT/0608040, ISBN 978-0-691-14049-0, MR 2522659
  9. ^ B. Toën, M. Vaquié, Moduli of objects in dg-categories. Ann. Sci. de l’ENS Volume 40 (2007) Issue 3, Pages 387-444.
  10. ^ B. Toën, M. Vaquié, T. Pantev, G. Vezzosi) Shifted symplectic structures. Publ. Math. Inst. Hautes Études Sci. 117 (2013), 271-328.
  11. ^ D. Calaque, B. Toën, M. Vaquié, T. Pantev, G. Vezzosi) Shifted Poisson structures. Journal of Topology.
  12. ^ ICM Plenary and Invited Speakers since 1897, International Mathematical Union, retrieved 2015-10-01.
  13. ^ Derived Algebraic Geometry and Deformation Quantization ICM-2014 (PDF)
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