Bonn-Luxembourg-Strasbourg Days:

Operads

University of Luxembourg, 4-5 October 2010
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Table of Contents

  • Aims and Scope
  • Schedule
  • Abstracts
  • Organizing Committee
  • Participants
  • Registration
  • Practical Information
  • Aims and Scope

    These two days are primarily aimed at gathering researchers from Bonn, Luxembourg and Strasbourg who share an interest about operadic methods. Of course any other interested person is welcome.

    Schedule



    Monday
    Tuesday

    10h-11h : M. Doubek (B.24 A)

    11h30-12h30 : J. Millès (B.24 A)
    15h30-16h30 : B. Vallette (B.04)
    12h30-15h30 : Lunch, free discussion (B.24 A)
    16h30-17h00 : Coffee break 15h30-16h30 : H. Strohmayer (B.04)
    17h00-18h00 : A. Lazarev (B.04) 16h30-17h00 :  coffee  break
    18h00-19h30 : Free discussion (B.04)
    17h-18h : Colloquium J.L. Loday (A.02)
    20h : Dinner


    Abstracts



  • Martin Doubek (Prague)

    Title : Gerstenhaber-Schack diagram cohomology from the operadic point of view

    Abstract : Gerstenhaber and Schack defined a cohomology theory for diagrams of associative algebras. We consider the coloured operad $A$ describing such diagrams and our aim is to construct operadic cohomology for $A$-algebras. Therefore we would like to find a free resolution of the coloured operad $A$. This problem is already well understood e.g. for a single morphism (of algebras over Koszul operads). But for more complicated diagrams, little is known. We first state a theorem on existence of such a resolution. It is partially explicit but not to the extend so that we are able to write down the cohomology for $A$-algebras. Then we show that the operadic cohomology can be generally expressed as an Ext functor in the category of operadic modules. Therefore it suffices to construct a free resolution of a specific operadic module. As an application, we prove that Gerstenhaber-Schack diagram cohomology is indeed operadic cohomology.

  • Andrey Lazarev (Leicester)

    Title : Curved algebras and curved graph complexes

    Abstract: Let O be a cyclic, or, more generally, modular, operad and consider its Feynman transform F(O). Without the usual stability conditions (which, for example, prevent O from being unital) the operad F(O) is rather different from what one is used to; in particular it is usually acyclic in all arities save the bottom one (corresponding to the graphs with no legs). The corresponding legless part, however, could have nontrivial homology and we compute it in the cases when O is the operad governing unital associative or unital commutative algebras. This amounts to computing the homology of commutative and ribbon graph complexes when one allows vertices of valences one and two. The algebras over F(O) can sometimes be interptered as curved infinity algebras and we discuss the problem of classifying such algebras. A complete answer could be given in the case of nontrivially curved A-infinity or L-infinity algebras.

  • Jean-Louis Loday (CNRS, Strasbourg)

    Title : "Hidden structures in homological algebra"

    Abstract : If a chain complex is equipped with some compatible algebraic structure, then its homology gets equipped with this algebraic structure. The surprise is that, in most cases, there is a hidden algebraic structure on this homology. We will give several elementary examples and show how the notions of spectral sequence, Connes boundary map B, A-infinity algebra and MacLane invariant of a crossed module come naturally out of this principle. I'll end up with a problem in biology.

  • Joan Millès (MPIM-Bonn, Germany and University of Nice, France)

    Title : Koszul complex = cotangent complex

    Abstract: We extend the Koszul duality theory of associative algebras to any type of algebras, or more precisely, to algebras over an operad. Recall that in the classical case, this Koszul duality theory relies on an important chain complex: the Koszul complex. We show that the cotangent complex, involved in the cohomology theory of algebras over an operad, generalizes the Koszul complex.

  • Henrik Strohmayer (Luxembourg)

    Title : Homotopy theory of homotopy properads

    Abstract : Homotopy properads generalize properads the way A-infinity algebras generalize associative algebras. In this talk we will begin with discussing transfer of homotopy properad structures. From this one can show that quasi-isomorphisms are invertible. We will then discuss implications of this on the homotopy category of homotopy properads.

  • Bruno Vallette (MPIM-Bonn, Germany and University of Nice, France)

    Title : Homotopy Batalin-Vilkovisky algebras

  • Abstract: In this talk, I will survey the recent developments on the homotopy theory of Batalin-Vilkovisky algebras. For instance, I will give three different resolutions of the operad encoding BV-algebras: the Koszul one, the minimal one and a relative one. I will give applications on the moduli space of genus 0 curves, Topological Conformal Field Theories, Vertex algebras and double loop spaces. Finally, I will extend Kontsevich formality theorem to the homotopy BV case, which includes the divergence operator.

    Organizers

  • Yael FREGIER (Luxembourg) < yael (dot) fregier (at) uni (dot) lu >
  • Martin SCHLICHENMAIER (Luxembourg) < martin (dot) schlichenmaier (at) uni (dot) lu >
  • Bruno VALLETTE (Bonn) < brunov (at) mpim-bonn (dot) mpg (dot) de >
  • Participants

    (up to now the following people registered)
    • Olivia Bellier (Nice)
    • Martin Doubek (Prague)
    • Yael Fregier (Luxembourg)
    • Laurent Hofer (Luxembourg)
    • Andrey Lazarev (Leicester)
    • Jean-Louis Loday (Strasbourg)
    • Joan Milles (Bonn)
    • Martin Schlichenmaier (Luxembourg)
    • Oleg Sheinman (Moscow) 
    • Henrik Strohmayer (Luxembourg)
    • Bruno Vallette (Bonn)

    Registration

    To register for the Conference please send an email to:
    < yael (dot) fregier (at) uni (dot) lu >

    Practical Information

    The workshop will be held in the Campus Kirchberg of the University of Luxembourg.

    How to reach the Campus kirchberg

    Rooms : B.O4, B.24 A and A.02 (see schedule).

    Travel

    By plane

    The Luxembourg airport is connected by regular flights to all main destinations.

    A regular bus service, operated by Flibco, connects the train station to the Frankfurt-Hahn airport, which is served by low-cost flights to many European destinations.

    By train

    See the websites of the Luxembourg rail company CFL, or SNCF, or Deutsche Bahn.

    Accomodation

    A list of hotels in Luxembourg is available here. There is also a youth hostel.


    Author: Yael Fregier.

    Date: 2010/09/08 12:00:21 PM

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