




Thursday  September 24 



Time 
Speaker/Title/Abstract 


12:30  14:00 
Registration 


14:00  15:00 
Steffen Sagave  Rigidification of homotopy coherent commutative multiplications In various contexts, the use of functors defined on the category I of finite sets and injections makes it possible to replace Einfinity objects by strictly commutative ones. For example, Einfinity spaces can be replaced up to weak equivalence by strictly commutative monoids in Idiagrams of spaces, and Einfinity quasicategories can be replaced up to weak equivalence by strictly commutative monoids in Idiagrams of simplicial sets. Building on the latter result, we show that every presentably symmetric monoidal infinitycategory is represented by a symmetric monoidal model category. This can be viewed as a rigidification result about multiplicative homotopy theories. (This is report on joint work with Christian Schlichtkrull, with Dimitar Kodjabachev, and with Thomas Nikolaus.) 


15:30  16:30 
Yannick Voglaire  Invariant connections and PBW theorem for homogeneous spaces of Lie groupoids Given a closed wide Lie subgroupoid A of a Lie groupoid L, i.e. a Lie groupoid pair, I will introduce an associated Atiyah class and explain how it is the obstruction to the existence of Linvariant fibrewise affine connections on the homogeneous space L/A. For Lie groupoid pairs with vanishing Atiyah class, I will show that the left Aaction on the quotient space L/A can be linearized, I will outline an alternative proof of a result of Calaque about the Poincaré–Birkhoff–Witt map for such objects, and explain an interpretation of the Molino class of foliations suggested by this approach. This is joint work with Camille LaurentGengoux. 


17:00  18:00 
Vladimir Hinich  Enriched infinity categories and enriched infinityoperads We suggest a definition of enriched category and enriched colored opeard in the infinitycategorical setting. The definition of enriched category is based on a (more or less obvious) notion of enriched quiver. 


18:00 
Dinner 






Friday  September 25 



Time 
Speaker/Title/Abstract 


10:00  11:00 
Yael Fregier  Homotopy moment map The symmetries of a Hamiltonian systems on a symplectic manifold can be, in the good cases, described in terms of a moment map. On the other hand, there exists a generalization of Hamiltonian mechanics for closed forms of degree greater or equal to two. This appears for example when one considers symplectic structures on loop spaces. The role of Poisson brackets is then played by an $L_\infty$ algebra. It is therefore natural to seek for the analogue of the notion of moment map in this setting. We have introduced, in a commun work with Martin Callies, Chris Rogers and Marco Zambon, the notion of moment map up to homotopy as an $L_\infty$ morphism between the Lie algebra encoding the symmetries and the „Poisson" $L_\infty$ algebra. In this new framework, the correspondence due to Atiyah and Bott between cocycles in equivariant cohomology and couples (moment map, symplectic form) can be extended. 


11:30  12:30 
Cornelia Vizman  Integrability of central extensions of the Poisson Lie algebra We present a geometric construction of some central S1extensions of the quantomorphism group of a compact symplectic prequantizable manifold. On the way we obtain central S1extensions of the group of exact strict contact transformations, and of the universal cover of the group of Hamiltonian diffeomorphisms. 


12:30  13:30 
Lunch 


14:30  15:30 
Benoit Fresse  Rational homotopy and intrinsic formality of $E_n$operads The theory of E_noperads has considerably developed since a decade. Let us mention, among other applications, the second generation of proofs of the Kontsevich formality theorem, based on the formality of $E_2$operads, which has hinted the existence of an action of the GrothendieckTeichmüller group on moduli spaces of deformationquantization of Poisson algebras, and the description of the GoodwillieWeiss approximations of embedding spaces in terms of functions spaces on structures associated to $E_n$operads. The goal of this talk is to explain an intrinsic formality statement which gives a rational homotopy characterization of $E_n$operads in topological spaces in terms of their homology when $n\geq 3$. Recall that the homology of an $E_n$operad is identified with the operad governing Poisson algebra structures of degree $n1$. I will show that any operad in topological spaces which has the same rational homology as an $E_n$operad for some $n\geq 3$, and is additionally equipped with an involutive isomorphism that mimicks the action of a hyperplane reflection in the case $n4$, is rationally weaklyequivalent to an operad in topological spaces which is determined by this homology operad of Poisson algebras of degree $n1$. This is a joint work with Thomas Willwacher." 


16:00  17:00 
João Nuno Mestre  Measures and volumes for differentiable stacks We explain how an extension of Haefliger's approach to transverse measures for foliations allows us to define and study measures and geometric measures (densities) on differentiable stacks. The abstract theory works for any differentiable stack, but it becomes very concrete for proper stacks  for example, when computing the volume associated with a density, we recover the formulas that are taken as definition by Weinstein. This talk is based on joint work with Marius Crainic. 


18:00 
Dinner 






Saturday  September 26 



Time 
Speaker/Title/Abstract 


10:00  11:00 
Matija Basic  Stable homotopy theory of dendroidal sets Dendroidal sets were introduced as combinatorial models for topological operads. After recalling the definition and history of dendroidal sets, we will explain how dendroidal sets also model connective spectra. We will introduce homology theory of dendroidal sets and show how to use it to identify spectra that are associated to some dendroidal sets. This is joint work with Thomas Nikolaus. 


11:30  12:30 
Marco Zambon  Linfinity actions An infinitesimal action of a Lie algebra on a manifold can be encoded by a Lie algebroid, called transformation Lie algebroid, which in turn gives rise to a graded manifold endowed with a homological vector field (i.e., a Qmanifold). We describe how a similar phenomenon occurs for actions of Linfinity algebras on graded manifolds, and provide some examples. The same holds even ion the more general context of actions of an Linfinity algebroid A. Many examples occur when A is a Lie algebroid, one of them being representations up to homotopy. This talk is based on work with R. Metha and on work in progress with O. Brahic. 
