Categorification in Algebraic Geometry


Project :

Derived algebraic geometry goes back to intersection theory and particularly to the famous Serre's intersection formula introduced in the 50'. This formula express an intersection number as an alternating sum of dimensions of the higher Tor's of the structure sheaves of two algebraic sub-varieties.
In the early 90', Kontsevich has pushed the story one step further by introducing the notion of quasi-manifolds and virtual fundamental classes in his treatment of the moduli space of stable maps for then purpose of enumerative geometry of curves. The theory of quasi-manifolds and virtual classes have evolved independently in the late 90'. On the one side Kapranov and Ciocan-Fontanine introduced the notion of dg-schemes as a formalization of the notion of quasi-manifold. On the other side virtual classes has been defined in great generality by Behrend and Fantechi based on the notion of obstruction theories. Both of these notions have a serious drawback: the lack of functoriality, which in practice implies technical complications as well as un- reachable constructions. This has led several authors to develop new foundations for the whole subject. These foundations are based on techniques from homotopical algebra and higher category theory making the subject extremely flexible and therefore extremely rich in examples.
In this project, we plan to use derived algebraic geometry to find hidden functoriality properties and also to define Gromov-Witten invariants in non-archimedian geometry. Moreover we plan to categorify Donaldson-Thomas invariants and study deformation quantization.

Open positions : one post-doc 1+1 in Angers

Profil: Candidates must show a strong background in algebraic geometry and/or algebraic topology, as well as strong interests in themes connected to the project: derived algebraic geometry, Gromov-Witten theory, mirror symmetry, quantization, infinity category.
starting:The position starts in September or October 2018, and is for one year (with a possibility of renewal for a second year).
Applications: ​Candidate must send their applications to
  • CV
  • research statement
  • name of 2 or 3 persons to contact for reference letters
  • Deadline : Deadline is 31st January.
    Review of applications will begin on February 1st, 2018; however, the positions will remain open until filled.

    Members of the project:

  • Damien Calaque, University of Montpellier, IMAG
  • Alessandro Chiodo, University of Pierre et Marie Curie, IMJ
  • Gregory Ginot, University of Paris 13, LAGA
  • Etienne Mann, University of Angers, LAREMA
  • Tony Pantev, University of Pennsylvannia, Math department
  • Marco Robalo, University Pierre et Marie Curie IMJ
  • Bertrand Toen, Univertity of Toulouse, IMT
  • Michel Vaquie, University of Toulouse, IMT
  • Gabriele Vezzosi, University of Firenze DMA
  • Tony Yue Yu, University of Paris Sud, LMO

  • Associated members of the project

  • Samuel Bach, University Vancouver, UBC
  • Antony Blanc, SISSA
  • Jérémy Guéré , University of Grenoble
  • Benjamin Hennion , University Paris Sud LMO
  • Mauro Porta, University of Strasbourg, IRMA
  • Alexis Roquefeuil, University of Angers
  • Claudia Scheimbauer, Oxford University, Mathematical Institute