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Laboratoire de Mathématiques J.A. Dieudonné
Université de Nice-Sophia Antipolis
Parc Valrose
06108 Nice Cedex 02, France
Office 611
Tél : (+33) 4 92 07 64 78


Project ANR SAT

The web page of the ANR Grant Project "Higher Structures in Algebra and Topology" (2014-2018) can be reached here.

Lecture notes

vir  Higher Algebra with Operads, British Mathematical Colloquim  (Sheffield, 2013).    
vir  Jean-Louis Loday, "Operads Period" [1991-2012], conference "The Mathematical Legacy of Jean-Louis Loday" (Strasbourg, 2013).    
vir  Higher Algebra via Rewriting of Trees, Conference for the 60th Birthday of Pierre-Louis Curien (Venice, 2013).    


vir  Algebraic Operads, with Jean-Louis Loday, 654 pages,
     Grundlehren der mathematischen Wissenschaften,
     Volume 346, Springer-Verlag (2012).


This book contains three main parts on Koszul duality theory,
algebraic operads and homotopical algebra respectively.

To download it (last draft): 
Algebraic Operads
To order it (final version):  Springer

Cover GL346


vir  Symmetric homotopy theory of operads, with Malte Dehling [40 pages].  
vir  Pre-Lie deformation theory, with Vladimir Dotsenko and Sergey Shadrin [31 pages].   
vir  Givental action and trivialisation of circle action, with Vladimir Dotsenko and Sergey Shadrin [26 pages].   
vir  Homotopy theory of homotopy algebras, [30 pages].   


vir  De Rham Cohomology and homotopy Frobenius manifolds, with Vladimir Dotsenko and Sergey Shadrin, Journal of the European Mathematical
Volume 17, Issue 2 (2015), 535–547 [13 pages].  
vir  Algebra + Homotopy = Operad, in "Symplectic, Poisson and Noncommutative Geometry", MSRI Publications 62 (2014), 101-162
[survey article, 59 figures, 31 exercises].  
vir  Higher Koszul duality for associative algebras, with Vladimir Dotsenko, Glasgow Mathematical Journal, 55 (2013), 55-74.   
vir  The minimal model of the Batalin-Vilkovisky operad, with Gabriel Drummond-Cole, Selecta Mathematica, Volume 19, Issue 1 (2013), 1-47. 
vir  Givental group action on Topological Field Theories and homotopy Batalin-Vilkovisky algebras, with Vladimir Dotsenko and Sergey Shadrin,
      Advances in Mathematics, Volume 236 (2013), 224-256.

vir  Homotopy Batalin-Vilkovisky algebras, with Imma Galvez-Carrillo and Andy Tonks, Journal of Noncommutative Geometry (2012),
Issue 3, Volume 6, 539-602.    
vir  Deformation theory of representation of prop(erad)s II, with Sergei Merkulov,
      Journal für die reine und angewandte Mathematik (Crelles Journal), Issue 636 (2009), pages 125-174.  
vir  Deformation theory of representation of prop(erad)s I, with Sergei Merkulov,
      Journal für die reine und angewandte Mathematik (Crelles Journal), Issue 634 (2009), pages 51-106.  
vir  Free monoid in monoidal abelian categories, Applied Categorical Structures, 17, Issue 1 (2009), 43-61.   
vir  Manin products, Koszul duality, Loday algebras and Deligne conjecture
      Journal für die reine und angewandte Mathematik (Crelles Journal)
Issue 620 (2008), pages 105-164.  
vir  A Koszul duality for props, Trans. Amer. Math. Soc. 359 (2007), 4865-4943.   
vir  Homology of generalized partition posets, Journal of Pure and Applied Algebra, Volume 208, Issue 2 (February 2007), 699-725.   
vir  Pointed and multi-pointed partitions of type A and B, with Frédéric Chapoton, J. Algebraic Combin. 23 (2006), no. 4, 295-316.  
vir  Koszul duality for PROPs, C.R.Acad.Sci Paris 338, 12 (July 2004), 909-914. 

Ph.D. Thesis and Habilitation

vir  Propérades en Algèbre, Topologie, Géométrie et Physique Mathématique (June 2009), "Habilitation à diriger des recherches".  
vir  Dualité de Koszul des PROPs  (December 2003), Ph.D thesis, preprint IRMA.   

Lecture notes

vir  Opérades en Algèbre, Géométrie et Physique-Mathématique, Colloquium Algèbre-Géométrie-Logique (Université de Lyon, 2009).   
vir  Homotopy Batalin-Vilkovisky algebras, Seminar on Algebra, Geometry and Physics (Manin seminar, MPIM, 2009).  
vir  Deformation theory of algebraic structures, Second Congrès Canada-France (Montréal, June 2008).   
vir  Deformation theory of morphisms, Trends in Noncommutative Geometry (Northwestern University, 18-24 May 2007).   


vir Joan Millès, maître de conférences (tenure position) at Toulouse University (since September 2011).
      Ph.D. thesis on "Algebras and Operads: cohomology, homotopy and Koszul duality" (defended June 3, 2010).

vir  Olivia Bellier, Teacher in High School (since September 2013).
      Ph.D. thesis on "Algebraic and homotopical properties of operads on Hopf algebras" (defended October 16, 2012).
vir  Malte Dehling, (Göttingen, unofficial coadvisor with Chenchang Zhu and Thomas Schick from September 2011).
      Ph.D student on the homotopy properties of Courant algebroids and on homotopy operads.
vir  Brice Legrignou, (Nice since September 2013).
      Ph.D. student from the ENS Paris working on operads, infinity-categories and infinity-operads

Fields of interest 

Algebra, Geometry, Topology, and Mathematical Physics.

Curriculum Vitae

You can find my curriculum vitae (October 2014) here.   


Working Group     Factorisation Algebras (2014-2015)

vir  Higher algebra (2013-2014)
vir  Drinfeld associators, Multiple Zeta Values, and Grothendieck-Teichmüller groups (2012)
vir  En Operads and Cyclic Deligne Conjecture (2008-2009)
vir  Coxeter Groups, Hyperplane Arragements and Hopf algebras (2007-2008)
vir  Model categories, André-Quillen (co)homology and Gamma-modules (2006-2007)
vir  Cohomology of finite and profinite groups (2005-2006)
vir  String Topology (2004-2005)


vir  Grothendieck-Teichmüller Groups, Deformation and Operads, Isaac Newton Institute for Mathematical Sciences (Cambridge),
        January-April 2013 (main organizer).    GDO website
        The statistics of the downloaded videos (talks) are available here: Statistics


vir  Operads, deformation quantization and higher structures (MPIM, Fall 2010)
  Passe-Partout (Nice 2008-2009)

Master class

vir  Koszul duality for operads and its applications in Deformation-Quantization and in Rational Homotopy Theory, 
      University of Copenhaguen, April 16-27, 2012.  
Web Page       
      Exercises:   Sheet I   Sheet II  Sheet III
vir  Homotopy theory of Batalin--Vilkovisky algebras,  Les Diablerets, January 2015.   Exercises  

Proceedings of the Conference Operads 2009

vir   Operads 2009, Séminaires et Congrès, volume 26 (SMF) 2011, coeditor with Jean-Louis Loday.  download the volume


  Homotopical Algebra, Operads and Grothendieck--Teichmüller groups, Nice, September 9-12, 2014.   website
  Bonn-Luxembourg-Strasbourg Days "Operads", University of Luxembourg, 4-5 October 2010.  Website
  Workshop "Operads and homotopy theory", University of Lille, August 23-28, 2010.  Website
vir  Thematic school and international conference on Operads, Cirm (Luminy), April 20-25 and 27-30, 2009.  Website
vir  Workshop on En-operads, University of Copenhagen , November 17-21 2008.  Website
  Workshop on props and operads, Montpellier University, Mai 22-23 2008.  Website
  K-Theory, Cyclic Homology and Operads, a Conference on the occasion of Jean-Louis Loday's XXth birthday.
      5-7 January 2006 IRMA Strasbourg (France),  WebsitePoster.


vir  Jean-Louis Loday, "Operads" Period [1993-2012], personal text dedicated to the memory of a giant gone far too early.    



vir  Mathematics 234:  Multiple Integration and Vector Calculus (Northwestern 2007).  Click here


Transhumance:  Logbook.


Last update: March 29, 2015.