Benoit Fresse's home page

Curriculum Vitae

Education and diplomas:

• 2002:Habilitation à diriger des recherches. Habilitation thesis defended on 3rd June 2002 at the University of Nice.
  Title: ``Operad structures in homological algebra''.
• 1994-1997:PhD in Sciences. Thesis defended on 4th December 1996 at Louis Pasteur's University (Strasbourg).
  Title: ``Cogroups in algebras over an operad''.
  Advisor: M. J.-L. Loday.
• 1993-1994:DEA in Mathematics at Denis Diderot's University (Paris).
• 1990-1993:Education at the École Polytechnique (Palaiseau).

Positions:

• 2003: Professor, University of Lille 1.
• 1998-2003: Maître de Conférences (Assistant Professor), University of Nice.
• 1997-98: ATER (Postdoc), University of Nice.
• 1994-97: Allocataire-Moniteur (Graduate Assistant), Louis Pasteur's University (Strasbourg).

Visiting positions, Temporary assignements:

• 2001-02:Temporary CNRS position at the University of Nice, 12 months.
• 1999:Invitation at Northwestern University, Evanston (USA), 1 month.

Work

Publications

1. Cogroupes dans les algèbre sur une opérade, Thèse de doctorat de l'Université Louis Pasteur (Strasbourg 1), 1996, 107 pages.
2. Opérations de Cartan pour les algèbres simpliciales sur une opérade, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), 247-252. MR 98c:18009
3. Lie theory of formal groups over an operad, J. of Algebra 202 (1998), 455-511. MR 99c:14063, Publication.
4. Homologie de Quillen pour les algèbres de Poisson, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), 1053-1058. MR 99j:16001
5. Cogroups in algebras over an operad are free algebras, Comment. Math. Helv. 73 (1998), 637-676. MR 99i:18010, Publication.
6. Algèbre des descentes et cogroupes dans les algèbres sur une opérade, Bull. Soc. Math. Fr. 126 (1998), 407-433. MR 2000c:16049, Publication.
7. On the homotopy of simplicial algebras over an operad, Trans. Amer. Math. Soc., 352 (2000), 4113-4141. MR 2000m:18015 Publication.
8. Structures de Poisson sur une intersection complète à singularitées isolées, C. R. Acad. Sci. Paris Sér. I Math. 335 (2002), 5-10. MR 2003g:13017, Publication.
9. Une décomposition prismatique de l'opérade de Barratt-Eccles, avec Clemens Berger, C. R. Acad. Sci. Paris Sér. I Math. 335 (2002), 365-370. MR 2003m:55006, Publication.
10. La construction bar d'une algèbre comme algèbre de Hopf E-infini, C. R. Acad. Sci. Paris Sér. I Math. 337 (2003), 403-408. MR 2004h:18008, Publication.
11. Combinatorial operad actions on cochains, avec Clemens Berger, Math. Proc. Cambridge Philos. Soc. 137 (2004), 135-174. MR2075046 (2005e:18013), Publication.
12. Koszul duality of operads and homology of partition posets, in "Homotopy theory and its applications (Evanston, 2002)", Contemp. Math. 346, Amer. Math. Soc. (2004), 115-215. MR2066499 (2005g:18015), Article en PDF.
13. Théorie des opérades de Koszul et homologie des algèbres de Poisson, Ann. Math. Blaise Pascal 13 (2006), 237-312. MR2275449 (2009b:17051), Publication.
14. Modules over operads and functors, Lecture Notes in Mathematics 1967, Springer Verlag, 2009, 318 pages.
    • Abstract
    • Publication
    • Manuscript (final version) in PDF
15. Operadic cobar constructions, cylinder objects and homotopy morphisms of algebras over operads, in "Alpine perspectives on algebraic topology (Arolla, 2008)", Contemp. Math. 504, Amer. Math. Soc. (2009), 125-189. Abstract, Article in PDF.
16. The bar complex of an E-infinity algebra, Adv. Math. 223 (2010), pp. 2049--2096. Abstract, Publication.
17. Props in model categories and homotopy invariance of structures, Georgian Math. J. (in press). Abstract, Publication, Manuscript (final version) in PDF.

Preprints in final form and submitted for publication

1. Iterated bar complexes of E-infinity algebras and homology theories, preprint (2008), 82 pages. Abstract, Article in PDF.
2. Koszul duality of E_n-operads, preprint (2009), 63 pages. Abstract, Article in PDF. Talk at the 3rd Arolla Topology Conference, Arolla, Switzerland (2008), Presentation in PDF.
3. On mapping spaces of differential graded operads with the commutative operad as target, preprint (2009), 16 pages. Abstract, Article in PDF.
4. Batanin's category of pruned trees is Koszul, preprint (2009), 44 pages. Abstract, Article in PDF.
5. Koszul duality complexes for the cohomology of iterated loop spaces of spheres, preprint (2010), 23 pages. Abstract, Article in PDF.

Work in progress

1. Homologie de Poisson de surfaces à une singularité isolée, notes (1998). Article en PDF.
2. Derived division functors and mapping spaces, preprint to be revised (2002), 34 pages. Abstract, Article in PDF.
3. The universal Hopf operads of the bar construction, memoir to be revised (2007), 125 pages. Abstract, Full text in PDF.
4. Le complexe bar itéré des E_n-algèbres comme un diagramme homotopique sur la catégorie des arbres élagués, preprint (2009), 67 pages. Abstract, Article in PDF.
5. Rational homotopy automorphisms of E_2-operads and the Grothendieck-Teichmuller group, in preparation. Abstract, Text in preparation in PDF.

Internal reports

1. Applications polynomiales et foncteurs polynomiaux, notes of a talk (1997), 24 pages. Full text in PDF.
2. Structures d'opérades en algèbre homologique, mémoire d'habilitation à diriger des recherches (2002), 36 pages. Full text in PDF.