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| Professor 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 vallette@math.univ-paris13.fr |
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BooksMaurer--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 |
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Operadic Calculus for Higher Colour-Kinematics Duality,
with Anibal M. Medina-Mardones,
ArXiv:2512.12948
[37 pages].
Pre-Calabi--Yau algebras and homotopy double Poisson gebras,
with Johan Leray,
ArXiv:2203.05062
[59 pages].
Effective integration of Lie type algebras,
Phil. Trans. R. Soc. A 384 20240409 (2026).
ArXiv:2006.01649 [19 pages].
Deformation theory of Cohomological Field Theories,
avec Vladimir Dotsenko, Sergey Shadrin et Arkady Vaintrob, Journal für die reine und angewandte Mathematik (Crelles Journal), Issue 809, 91-157 (2024).
ArXiv:2006.01649
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
Symmetric
homotopy theory of operads,
with
Malte Dehling, Algebraic
Geometry and Topology, 21
(2021), 1595–1660,
ArXiv:1503.02701
Monoidal
structures on the categories of quadratic data,
with
Yuri I. Manin, Documenta
Mathematica 25, 1727-1786 (2020). ArXiv:1902.03778
Properadic
homotopical calculus,
with
Eric Hoffbeck and Johan Leray,
IMRN (2020), ArXiv:1910.05027
[61 pages].
Homotopy
theory of homotopy algebras,
Annales de l'Institut Fourier, 70 (2020) 683-738, ArXiv:1411.5533
[54 pages].
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.
Brown's
moduli spaces of curves and the gravity operad,
with
Clément Dupont, Geometry
& Topology, 21 (2017), no. 5, 2811–2850.
Pre-Lie
deformation theory,
with
Vladimir Dotsenko and Sergey Shadrin, Moscow Mathematical Journal, Volume
16, Issue 3 (2016) 505-543
Givental
action and
trivialisation of circle action,
with
Vladimir Dotsenko and Sergey Shadrin,
Journal de
l’École polytechnique – Mathématiques, 2 (2015), 213-246.
De
Rham Cohomology and homotopy Frobenius manifolds, with
Vladimir Dotsenko and Sergey Shadrin, Journal of the European Mathematical
Algebra
+ Homotopy = Operad, in
"Symplectic, Poisson and Noncommutative Geometry", MSRI Publications 62
(2014), 101-162 [survey
article, 59 figures, 31 exercises].
Higher
Koszul duality for associative algebras, with
Vladimir Dotsenko, Glasgow Mathematical Journal,
55 (2013), 55-74.
The
minimal model of the Batalin-Vilkovisky operad, with
Gabriel Drummond-Cole, Selecta
Mathematica, Volume 19, Issue 1 (2013),
1-47.
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.
Homotopy
Batalin-Vilkovisky algebras,
with
Imma Galvez-Carrillo and Andy Tonks, Journal
of Noncommutative Geometry (2012),
Issue 3,
Volume 6, 539-602. 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.
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.
Free
monoid
in monoidal abelian categories,
Applied Categorical Structures, 17, Issue 1 (2009),
43-61. Manin
products, Koszul duality, Loday algebras and Deligne conjecture,
Journal für die reine und angewandte Mathematik (Crelles Journal)
Issue 620 (2008), pages 105-164.
A
Koszul duality for props, Trans.
Amer. Math. Soc. 359 (2007), 4865-4943.
Homology
of
generalized partition posets, Journal
of Pure and Applied Algebra, Volume 208, Issue 2 (February 2007),
699-725.
Pointed
and
multi-pointed partitions of type A and B,
with Frédéric
Chapoton, J. Algebraic Combin. 23 (2006), no. 4, 295-316.
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.
Propérades
en Algèbre, Topologie, Géométrie et Physique Mathématique
(June 2009),
"Habilitation à diriger des recherches".
Dualité
de
Koszul des PROPs (December 2003),
Ph.D
thesis, preprint IRMA.
Opérades
en Algèbre, Géométrie et Physique-Mathématique, Colloquium
Algèbre-Géométrie-Logique (Université de Lyon, 2009).
Homotopy
Batalin-Vilkovisky algebras,
Seminar on Algebra, Geometry and Physics (Manin seminar, MPIM,
2009). Deformation
theory of algebraic structures,
Second Congrès Canada-France (Montréal, June 2008). Deformation
theory of morphisms, Trends
in Noncommutative Geometry (Northwestern University, 18-24 May
2007).
Ibrahim El Agami, Ph.D thesis on the homotopy theory of bialgebras and applications (since September 2025, grant from the graduate school of the USPN).
Mathieu
Vallée,
Postdoctoral student at the Max Planck Institute Institute for Mathematics in the Sciences (Leibzig, Germany),
Coline
Emprin,
Postdoctoral student at Stockholm University,
Victor
Roca Lucio,
Postdoctoral student at Université Paris Cité,
Guillaume Laplante Anfossi
postdoctoral student at Southern Denmark University (Denmark),
Daniel
Robert-Nicoud,
Data Scientist at Laval Science (Zürich).
Malte
Dehling,
PhD student
(defended November 16, 2020; coadvisor: Chenchang Zhu),
Brice
Legrignou,
Engineer in Shift Technology (since September 2019),
Olivia
Bellier, Teacher in Classes Prépartoires at Toulouse (since
September 2013).
Joan
Bellier-Millès,
maître de
conférences (tenure position) at Toulouse University (since September
2011).
Anibal
Medina-Mardones,
postdoctoral grant from the ANR HighAGT project (2022-2023).
Felix
Wierstra,
postdoctoral grant from the Swedish Research Council (2019-2021). [Tenure
track, University of Amsterdam.]
Ricardo
Campos, postdoc
supported by a grant from the Swiss National Fund (2017-2018).
[CR CNRS, University of Montpellier.]
Johan
Leray, postdoctoral
student support by grant DIM Math Innov, supervised with Gregory Ginot
(2018-2020).
[ATER
University of Nantes]
Grothendieck--Teichmüller
groups and applications (2020-2021)
Mandell's
theorem (2019)
Persitant
homology and Topological Data Analysis (2018-2019)
Factorisation
Algebras and Factorisation Homology (2017-2018)
Infini-categories
(2016-2017)
Factorisation
Algebras (2014-2015)
Higher
algebra (2013-2014)
Drinfeld
associators, Multiple Zeta Values, and Grothendieck-Teichmüller groups
(2012)
En
Operads and Cyclic Deligne Conjecture (2008-2009) Coxeter
Groups, Hyperplane Arragements and Hopf algebras (2007-2008) Model
categories, André-Quillen (co)homology and Gamma-modules
(2006-2007) Cohomology
of finite and profinite groups (2005-2006)
String
Topology (2004-2005)
Higher
homotopical structures, CRM
(Barcelona), January-July
2021 & June-July 2022. HHS
website
Grothendieck-Teichmüller
Groups, Deformation and Operads, Isaac
Newton Institute for Mathematical Sciences (Cambridge),
The
web page of the ANR PRC Grant
"Higher Algebra, Geometry, and Topology" (2021-2026) can be reached
here.
The
web page of the ANR JCJC Grant "Higher
Structures in Algebra and Topology" (2014-2019) can be reached here.
Operads,
deformation quantization and higher structures (MPIM, Fall 2010)
Passe-Partout
(Nice 2008-2009)
Koszul
duality for operads and its applications in Deformation-Quantization and
in Rational Homotopy Theory,
Homotopy
theory of Batalin--Vilkovisky algebras, Les
Diablerets, January 2015.
Exercises
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 Thematic
school and international conference on Operads, Cirm
(Luminy), April 20-25 and 27-30, 2009. Website 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.
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
Mathematics
234: Multiple Integration and Vector Calculus
(Northwestern 2007). Web
page
Last update: September 2, 2026.
