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

*Fano fourfolds of K3 type*(with E. Fatighenti, L. Manivel and F. Tanturri), preprint: ArXiv:2111.13030.*Nested varieties of K3 type*(with E. Fatighenti and L. Manivel), J. Éc. Polytech., Math. 8, 733-778 (2021).*A categorical invariant for geometrically rational surfaces with a conic bundle structure*(with S. Durighetto), preprint: ArXiv:1909.12647.*Categorical dimension of birational automorphisms and filtrations of Cremona groups*, Journal of the Math. Soc. of Japan 73, No. 3, 861-883 (2021).*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).*Bridgeland Stability Conditions on Fano Threefolds*(with E. Macrì, B. Schmidt, and X. Zhao), Épijournal de Géométrie Algébrique Vol 1 (2017).*Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields*(with A. Auel), Proc. London Math. Soc. (3) 117 (2018) 1-64.*Homological projective duality for determinantal varieties*(with M.Bolognesi and D.Faenzi), Adv. Math. 296, 181-209 (2016).*Some remarks concerning Voevodsky's nilpotence conjecture*(with M.Marcolli and G.Tabuada), J. Reine Angew. Math. 738 (2018), 299-312.*Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives*(with G.Tabuada), Izvestiya: Mathematics 80, no. 3 (2016) , preprint: ArXiv:1310.6020.*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).*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.*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.*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).*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).*Derived categories and rationality of conic bundles*(with M. Bolognesi), Comp.Math 149 (11), 1789-1817 (2013).*The Euclid-Fourier-Mukai algorithm for elliptic surfaces*(with G. Hein) Asian J. of Math 18 (2), 345-364 (2014).*A categorical invariant for cubic threefolds*(with E. Macrì, S. Mehrotra, and P. Stellari), Adv. Math. 229 (2), 770-803 (2012).*Stable pairs on elliptic K3 surfaces*, C. R. Acad. Sci. Paris, Ser. I 348 (2010).*Fourier-Mukai transforms of curves and principal polarizations*, C. R. Acad. Sci. Paris, Ser. I 345 (2007).*A semiorthogonal decomposition for Brauer-Severi schemes*, Math. Nachr. 282, No. 10, 1406-1413 (2009).*Calabi-Yau complete intersections with infinitely many lines*, Rend. Semin. Mat. Univ. Politec. Torino, 66 (2008), no 2.

## Theses

- My Habilitation Thesis,
*Semiorthogonal decompositions and noncommutative motives in algebraic geometry*, discussed on 21st October 2016. - My PhD Thesis,
*Catégories dérivées, espaces de modules*, discussed on 23rd June 2008, under the direction of Arnaud Beauville.

## 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**

- FRG/CIMI Workshop on semiorthogonal decompositions, stability conditions and derived categories, IMT, Toulouse, 2-5 May 2018.
- Summer school and conference
*New methods in Birational Geometry*, Toulouse, June 2016. - 2015 yearly meeting of the french Algebraic Topology network GDR Topologie algébrique et ses applications, Toulouse, October 2015.
- Summer school
*Derived categories*, Nantes, June 2014.

## 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.