Head Giacometti


Mathematical website of

Bruno VALLETTE


 

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Permutoedre

Laboratoire de Mathématiques J.A. Dieudonné
Université de Nice-Sophia Antipolis
Parc Valrose
06108 Nice Cedex 02, France
Bureau 622
Tél : (+33) 4 92 07 62 61
brunov@[antispam]unice.fr
U-Nice



Programme

vir  Grothendieck-Teichmüller Groups, Deformation and Operads, Isaac Newton Institute for Mathematical Sciences (Cambridge),
        January-April 2013 (main organizer, so feel free to contact me. It is right now!).    GDO website

Lecture notes

vir  Higher Algebra with Operads, British Mathematical Colloquim  (Sheffield, 2013).    

Miscellaneous

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

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Book


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

Preprints

vir  Homotopy theory of homotopy algebras, [25 pages].   
vir  De Rham Cohomology and homotopy Frobenius manifolds, with Vladimir Dotsenko and Sergey Shadrin, to appear in Journal of the European Mathematical
      Society [11 pages]. 
ArXiv:1203.5077
vir  Algebra + Homotopy = Operad,  introduction to operads and to homotopical algebra [59 figures, 30 exercises, 43 pages, to appear in the proceedings of the MSRI
      and
RIMS "Symplectic Geometry, Noncommutative Geometry and Physics"]. ArXiv:1202.3245

Publications

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  Higher Koszul duality for associative algebras, with Vladimir Dotsenko, to appera in Glasgow Mathematical Journal [15 pages].  ArXiv:1201.6509
vir  Givental group action of Topological Field Theories and homotopy Batalin-Vilkovisky algebras, with Vladimir Dotsenko and Sergey Shadrin, to appear in
      Advances in Mathematics
[28 p]. ArXiv:1112.1432
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).   

Students

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, ATER (postdoc position) at Toulouse University (since September 2012).
     Ph.D. thesis on "Algebraic and homotopical properties of operads on Hopf algebras" (defended October 16, 2012).
vir Malte Dehling, (Göttingen, coadvisor with Chenchang Zhu from September 2011).
     Ph.D student on the homotopy properties of Courant algebroids and on homotopy operads.

Fields of interest 

Algebra, Geometry, Topology, Logic, and Mathematical Physics.

Curriculum Vitae

You can find my curriculum vitae (December 2012) here.   

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Working Group     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)

Seminar

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

Proceedings of the Conference Operads 2009

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

 Conferences 

  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.

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Teaching 

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

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Transhumance:  Logbook.

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Last update: January 6, 2013.