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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 Junior member of the Institut Universitaire de France (2016-2021) |
 
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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 List of corrections (to be typed): Erratum |
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Pre-Calabi--Yau
algebras and homotopy double Poisson gebras,
with Johan
Leray, ArXiv:2203.05062
[43 pages].
Deformation
theory of Cohomological Field Theories,
with
Vladimir
Dotsenko, Sergey
Shadrin et Arkady Vaintrob, ArXiv:2006.01649
[57 pages].
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).
Mathieu
Vallée,
Ph.D. student (since September 2022, coadvisor:
Roland Grappe),
Coline
Emprin,
Ph.D. student (since September 2021, coadvisor:
Geoffroy Horel),
Victor
Roca Lucio,
Ph.D student (since September 2019),
Guillaume
Laplante Anfossi,
PhD student
(since September 2019, coadvisor: Eric Hoffbeck),
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]
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),
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: January
27, 2023.
