Head Giacometti

Mathematical website of


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Laboratoire Analyse, Géométrie et Applications

Université Sorbonne Paris Nord
Institut Galilée
99, Avenue Jean-Baptiste Clément
93430 Villetaneuse, France
Bureau D412
Tél : (+33) 1 49 40 35 85

Junior member of the Institut Universitaire de France 



Projet ANR HighAGT

Website of the project ANR PRC "Higher Algebra, Geometry, and Topology" (2021-2024)


Operadic renormalisation group, conference "Higher structures in Renormalisation" (2020) Video  
Deformation theory of cohomological field theories, talk at the conference "Operad Pop-Up" (2020) Video
Operads and Koszul duality, Course given during the GDO programme (Newton Institute, Cambrige, 2013)
Introduction, Operads, Koszul duality for algebras, Koszul duality for operads,
Methods for Koszul duality, Homotopy algebras, Deformation theory

Lecture notes

Why Higher structures? Math+ Berlin Colloquium (January 2023) 
Why Higher structures? Antwerp Algebra Colloquium (2020)    Video           
Operadic renormalisation group
, conference "Higher structures in Renormalisation" ("Vienna", 2020)  
Deformation theory of cohomological field theories, conference "Operad Pop-Up" (2020).
Higher Algebra with Operads, British Mathematical Colloquim  (Sheffield, 2013)    
Jean-Louis Loday, "Operads Period" [1991-2012]
,  "The Mathematical Legacy of Jean-Louis Loday" (Strasbourg, 2013)    


Maurer--Cartan methods in deformation theory: the twisting procedure, with Vladimir Dotesnko and Sergey Shadrin, 181 pages, London Mathematical Society Lecture Note Series, Cambridge University Press (2023).  

This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment of the twisting procedure, which functorially creates new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer-Cartan element.

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

List of corrections (to be typed): Erratum

Cover GL346


vir  Pre-Calabi--Yau algebras and homotopy double Poisson gebras, with Johan Leray, ArXiv:2203.05062 [43 pages].   
vir  Higher Lie theory, with Daniel Robert-Nicoud, ArXiv:2010.10485 [89 pages].   
vir  Deformation theory of Cohomological Field Theories, with Vladimir Dotsenko, Sergey Shadrin et Arkady Vaintrob, ArXiv:2006.01649 [57 pages].   


vir  The diagonal of the associahedra, with Naruki Masuda, Hugh Thomas, and Andy Tonks, Journal de l’École polytechnique 8, 121-146 (2021). ArXiv:1902.08059  
vir  Symmetric homotopy theory of operads, with Malte Dehling, Algebraic Geometry and Topology, 21 (2021), 15951660, ArXiv:1503.02701
vir  Monoidal structures on the categories of quadratic data, with Yuri I. Manin, Documenta Mathematica 25, 1727-1786 (2020). ArXiv:1902.03778  
vir  Properadic homotopical calculus, with Eric Hoffbeck and Johan Leray, IMRN (2020), ArXiv:1910.05027 [61 pages].   
vir  Homotopy theory of homotopy algebras, Annales de l'Institut Fourier, 70 (2020) 683-738, ArXiv:1411.5533 [54 pages].   
vir  Toric varieties of Loday’s associahedra and noncommutative cohomological field theories, with Vladimir Dotsenko and Sergey Shadrin, Journal of Topology, Volume 12, Issue 2, (2019), 463-535.   
vir  Brown's moduli spaces of curves and the gravity operad, with Clément Dupont, Geometry & Topology, 21 (2017), no. 5, 2811–2850.
vir  Pre-Lie deformation theory, with Vladimir Dotsenko and Sergey Shadrin, Moscow Mathematical Journal, Volume 16, Issue 3 (2016) 505-543
vir  Givental action and trivialisation of circle action, with Vladimir Dotsenko and Sergey Shadrin, Journal de l’École polytechnique – Mathématiques, 2 (2015), 213-246.  
vir  De Rham Cohomology and homotopy Frobenius manifolds, with Vladimir Dotsenko and Sergey Shadrin, Journal of the European Mathematical
      Society, 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. 

In order to support public research, I now submit my articles only to (free) academic journals.

My research works are 100% funded by public institutions; we edit and refer freely the research articles for publication, which often appear in electronic format.
So there is no reason for the Government to pay high fees to private edition compagnies so that the mathematical community  can have an acces to its own work.

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  Mathieu Vallée, Ph.D. student (since September 2022, coadvisor: Roland Grappe),
      Ph.D Thesis in computer science on integer polytopes (doctoral grant from MathStic project).
vir  Coline Emprin, Ph.D. student (since September 2021, coadvisor: Geoffroy Horel),
      Ph.D Thesis on homotopical algebra, operadic calculus, and formality (doctoral grant from ENS Paris).
vir  Victor Roca Lucio, Ph.D student (since September 2019),
      Ph.D Thesis on operads and rational homotopy (doctoral grant from the University Paris 13).
vir  Guillaume Laplante Anfossi, PhD student (since September 2019, coadvisor: Eric Hoffbeck),
      Ph.D Thesis on diagonals of polytopes and homotopy operads (doctoral grant Cofund MathInParis from the FSMP).
vir  Daniel Robert-Nicoud, Data Scientist at Laval Science (Zürich).
      Ph. D. thesis on "Operads and Maurer--Cartan elements" supported by a grant DIM RDF IdF (defended June 22, 2018).
vir  Malte Dehling, PhD student (defended November 16, 2020; coadvisor: Chenchang Zhu),
      PhD Thesis on operads and homotopy Lie algebras over Z (grant of Göttingen University).
vir  Brice Legrignou, Engineer in Shift Technology (since September 2019),
      Ph.D. thesis funded by the ENS Paris on "The homotopy theories of unital algebras and operads" (defended September 14, 2016).
vir  Olivia Bellier, Teacher in Classes Prépartoires at Toulouse (since September 2013).
      Ph.D. thesis on "Algebraic and homotopical properties of operads on Hopf algebras" (defended October 16, 2012).
vir Joan Bellier-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  Anibal Medina-Mardones, postdoctoral grant from the ANR HighAGT project (2022-2023).
vir  Felix Wierstra, postdoctoral grant from the Swedish Research Council (2019-2021). [Tenure track, University of Amsterdam.]
vir  Ricardo Campos, postdoc supported by a grant from the Swiss National Fund (2017-2018). [CR CNRS, University of Montpellier.]
vir  Johan Leray, postdoctoral student support by grant DIM Math Innov, supervised with Gregory Ginot (2018-2020). [ATER University of Nantes]

Fields of interest 

Algebra, Geometry, Topology, and Mathematical Physics.

Curriculum Vitae

You can find my curriculum vitae (February 2017) here.   


Working Group     Grothendieck--Teichmüller groups and applications (2020-21)

vir  Mandell's theorem (2019)
vir  Persitant homology and Topological Data Analysis (2018-2019)
vir  Factorisation Algebras and Factorisation Homology (2017-2018)
vir  Infini-categories (2016-2017)
vir  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  Higher homotopical structures, CRM (Barcelona), January-July 2021 & June-July 2022. HHS website
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

Project ANR SAT

The web page of the ANR Grant Project "Higher Structures in Algebra and Topology" (2014-2019) can be reached here.


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


  Barcelona conference on Higher Structures, Universitat de Barcelona, 13-17 June 2022.   website
  Higher structures and operadic calculus, CRM Barcelona, 21-25 June 2021.   website
  Higher Structures, CIRM (Luminy),  January 21-25, 2019.   website Higher Structures Day, University Paris 13,  June 21, 2018.   website
  Arbeitstagung 2017 on "Physical Mathematics" in honor of Yuri Ivanovich Manin, MPIM Bonn, June 19-23, 2017.   website
  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.    



  Homotopy theories: Master II course (Paris, November-December).  2018 , 2020 & 2021
  Algebra + Homotopy = Operads: Master II course (Paris, November-December 2017).  Web page
vir  Mathematics 234:  Multiple Integration and Vector Calculus (Northwestern 2007).  Web page


Last update: January 27, 2023.