Publications and preprints

Click on a title to see its abstract

  1. Categorical dimension of birational automorphisms and filtrations of Cremona groups, preprint: ArXiv:1701.06803.

  2. Cycles, derived categories, and rationality (with A. Auel), in Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics 95, 199-266 (2017).pdf

  3. Bridgeland Stability Conditions on Fano Threefolds (with E. Macrì, B. Schmidt, and X. Zhao), Épijournal de Géométrie Algébrique Vol 1 (2017).pdf

  4. Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields (with A. Auel), Proc. London Math. Soc. (3) 117 (2018) 1-64.pdf

  5. Homological projective duality for determinantal varieties (with M.Bolognesi and D.Faenzi), Adv. Math. 296, 181-209 (2016). pdf

  6. Some remarks concerning Voevodsky's nilpotence conjecture (with M.Marcolli and G.Tabuada), J. Reine Angew. Math. 738 (2018), 299-312.pdf

  7. Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives (with G.Tabuada), Izvestiya: Mathematics 80, no. 3 (2016) pdf, preprint: ArXiv:1310.6020.

  8. From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives (with G.Tabuada), Moscow Math. Journal 16 (2), pp. 205-235 (2016). pdf

  9. Relations between the Chow motive and the noncommutative motive of a smooth projective variety (with G.Tabuada), Journal of Pure and Applied Algebra 219 (2015), pp. 5068-5077. pdf

  10. Cubic fourfolds containing a plane and a quintic del Pezzo surface (with A. Auel, M. Bolognesi, and A. Várilly-Alvarado), Algebraic Geometry 2 (2014) 181-193. pdf

  11. Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems (with A. Auel, and M. Bolognesi), Journal de Math. Pures et Appliquées 102, 249-291 (2014). pdf

  12. Categorical representability and intermediate Jacobians of Fano threefolds (with M. Bolognesi), in Derived Categories in Algebraic Geometry, EMS Series of Congress Reports, 1-25 (2012). pdf

  13. Derived categories and rationality of conic bundles (with M. Bolognesi), Comp.Math 149 (11), 1789-1817 (2013). pdf

  14. The Euclid-Fourier-Mukai algorithm for elliptic surfaces (with G. Hein) Asian J. of Math 18 (2), 345-364 (2014). pdf

  15. A categorical invariant for cubic threefolds (with E. Macrì, S. Mehrotra, and P. Stellari), Adv. Math. 229 (2), 770-803 (2012). pdf

  16. Stable pairs on elliptic K3 surfaces, C. R. Acad. Sci. Paris, Ser. I 348 (2010). pdf

  17. Fourier-Mukai transforms of curves and principal polarizations, C. R. Acad. Sci. Paris, Ser. I 345 (2007). pdf

  18. A semiorthogonal decomposition for Brauer-Severi schemes, Math. Nachr. 282, No. 10, 1406-1413 (2009). pdf

  19. Calabi-Yau complete intersections with infinitely many lines, Rend. Semin. Mat. Univ. Politec. Torino, 66 (2008), no 2. pdf


Posters and Beamer presentations

  • My Poster at the Cremona Conference in Basel, September 2016.
  • A talk about cubic surfaces, 27 lines, and the icosahedron in Courant Institute, New York City, November 2012.
  • My Poster at the Nachwuchskonferenz in Mainz, November 2010.



  • Je suis responsable du L3 Parcours spécial math.
  • Algèbre - L3 ESR et L3 Spécial.
  • Théorie de Hodge - M2 Math Fonda.
  • Algèbre - Cours intensif - L3 Spécial.
  • TD Géometrie - L2 Math.
  • Cours et TD Algèbre - L1 Math.

  • 2016-2017

    • Algèbre Linéaire 2 - M1 CMI-SID. Le poly du cours.
    • TD Algèbre - L3 Spécial. Les feuilles de TD: TD1, TD2, TD3, TD4, TD5.
    • TD Mathématiques - L1 Chimie. Les TD: Partie1 (fonctions), Partie2 (nombres complexes), Partie3 (polynômes).
    • Théorie de Hodge - M2 Math Fonda.
    • Algèbre - Cours intensif - L3 Spécial.
    • TD Géometrie - L2 Math.
    • Cours et TD Algèbre - L1 Math.


    • Cours et TD Algèbre - L3 Spécial.
    • Algèbre Linéaire - M1 CMI-SID.


    • Mathématiques - L1 Cap Réussite.
    • Algèbre Linéaire - L3 CMI-SID.
    • TD Algèbre - L3 Spécial.
    • Algèbre Linéaire 2 - M1 CMI-SID.


    • Histoire des Mathématiques - L3 MMESI.
    • Math2 - L1 SFA, Groupe C3.
    • Outils Math - L1 SN, Groupe D1.
    • Algèbre Linéaire - L3 CMI-SID.
    • TD Algèbre - L3 Spécial.


    • TD Algèbre Commutative - M1 MATH FONDA.
    • MATH 2 - L1, Groupe C4.


    • TD Algèbre Commutative - M1 MATH FONDA.
    • MATH 2 - L1, Groupe E3.

The weekly seminar Homotopie en Géométrie Algébrique at the Institut de Mathématiques de Toulouse.

PhD Students


  • Responsable du L3 - Math (parcours spécial).
  • Membre du comité de pilotage du GDR GAGC.
  • Membre du conseil scientifique de prospective (CSP) de l'Institut de Mathématiques de Toulouse.
  • Membre du conseil de pôle "MSTII" de l'Université Paul Sabatier.

Short CV


  • 2017: Lectures on Derived categories, semiorthogonal decomposition, and rationality at the winter (july) school Derived Categories at the Pontifica Universidàd Catòlica de Santiago de Chile.
  • 2016: Lectures at the FRG winter school Unramified cohomology, derived categories and rationality at the University of Utah.
  • 2014: IPMU (Tokyo), Osaka University.
  • 2013: E.Schrödinger Institut (Vienna).
  • 2012: Courant Institute at NYU, Ohio State University (Columbus).
  • 2010: RIMS (Kyoto).
  • 2009: University of Utah (Salt Lake City).


  • 2016, October: Habiltation thesis Semiorthogonal decompositions and noncommutative motives in algebraic geometry, Université Paul Sabatier.
  • since 2011: Maître de conférences at the Université Paul Sabatier, Toulouse.
  • 2009-2011: Post-doc fellow at the University of Duisburg-Essen.
  • 2008-2009: Post-doc fellow at the University of Bonn.
  • 2008, June: Ph.D. thesis Catégories dérivées, espaces de modules, Université de Nice - Sophia Antipolis.
  • 2004-2008: Ph.D. student at University of Nice - Sophia Antipolis. Advisor: Arnaud Beauville.
  • 2003-2004: DEA de Mathématiques at the University of Nice - Sophia Antipolis.
  • May-June 2003: Pre-doc visiting at the University of Utrecht.
  • 1998-2003: Laurea in Matematica at the University of Milan. Final dissertation: "Lines on CY varieties"

Organized events

The weekly algebraic geometry seminar in Toulouse: Homotopie en Géométrie Algébrique, on Tuesday, at 2pm.


Email adress: mbernard [at] math [punkt] univ-toulouse [point] fr

Mailing adress: Institut de mathématiques de Toulouse
Université Paul Sabatier
118 route de Narbonne
31062 Toulouse CEDEX 9 (France).

Office: Office number 138, bâtiment 1R2.

Telephone: +33 (0) 5 61 55 87 59.