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

Publications and preprints

Click on a title to see its abstract



  1. Fano fourfolds of K3 type (with E. Fatighenti, L. Manivel and F. Tanturri), preprint: ArXiv:2111.13030.

  2. Nested varieties of K3 type (with E. Fatighenti and L. Manivel), J. Éc. Polytech., Math. 8, 733-778 (2021)pdf.

  3. A categorical invariant for geometrically rational surfaces with a conic bundle structure (with S. Durighetto), preprint: ArXiv:1909.12647.

  4. Categorical dimension of birational automorphisms and filtrations of Cremona groups, Journal of the Math. Soc. of Japan 73, No. 3, 861-883 (2021)pdf.

  5. 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

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

  7. 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

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

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

  10. 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.

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

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

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

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

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

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

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

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


Theses



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.



Enseignements

2021-2022

  • Je suis responsable du L3 Parcours spécial math et de la L3 ESR.
  • Algèbre - L3 ESR et L3 Spécial.
  • TD Histoire des Maths - L2 Math.
  • Cours et TD Mathématiques - L1 spécial Math.
  • Algèbre - Cours intensif - L3 Spécial.


2020-2021

  • Je suis responsable du L3 Parcours spécial math.
  • Algèbre - L3 ESR et L3 Spécial.
  • TD Histoire des Maths - L2 Math.
  • Cours et TD Mathématiques - L1 spécial Math.
  • TP Math. discrètes - L1 Math.
  • Algèbre - Cours intensif - L3 Spécial.

2019-2020

  • Je suis responsable du L3 Parcours spécial math.
  • Algèbre - L3 ESR et L3 Spécial.
  • TD Histoire des Maths - L2 Math.
  • TD Mathématiques - L1 Math.

2018-2019

  • Je suis responsable du L3 Parcours spécial math.
  • Algèbre - L3 ESR et L3 Spécial.
  • Cours et TD de mathématiques - L1 Spécial.
  • Algèbre - Cours intensif - L3 Spécial.
  • TD Histoire des Maths - L2 Math.
  • TD Mathématiques - L1 Math.

2017-2018

  • 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.

2015-2016

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

2014-2015

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

2013-2014

  • 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.

2012-2013

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

2011-2012

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



PhD Students

  • Jordi Hernandez Gomez, Université Paul Sabatier (codirection with M. Spivakovsky), ongoing.
  • Dominique Mattei, Université Paul Sabatier, 2021.
  • Sara Durighetto, Università di Ferrara (codirection with M. Mella), 2019.

Tasks

  • Responsable du L3 - Math (parcours spécial et ESR).
  • Membre du comité égalité de l'Institut de Mathématiques de Toulouse.
  • Membre du conseil de Bibliothèque de l'Institut de Mathématiques de Toulouse.

Short CV

Visiting

  • 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).

Academic

  • 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




Contact

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.