The seminar usually takes place on Mondays, 10h45.

Current organiser: Pedro Vaz

Past organisers: Federico Cantero Morán (2015-16), Pedro Boavida de Brito and Paul Arnaud Tsopméné (2014 - 2015), Urtzi Buijs Martín (2013 - 2014).

2016/17

 10 Oct 2016 10h45 CYCL08 Daniel Tubbenhauer (U. Bonn) Some first steps towards 2-representation theory of Coxeter groups or: The 'next generation' of representation theory of Coxeter groups!? 09 Nov* 2016 16h45 CYCL03 Marco Mackaay (U. Algarve) The 2-representation theory of Soergel bimodules 28 Nov 2016 10h45 CYCL03 Paul Wedrich (Imperial College) Some differentials on colored Khovanov-Rozansky link homology 05 Dec* 2016 10h45 room CYCL09 Adam-Christiaan Van Roosmalen (U. Hasselt) Infinite acyclic cluster categories and their combinatorics

* - Joint with the Séminaire de théorie des catégories

2016

 15 Feb 2pm CYCL08 Pascal Lambrechts (UC Louvain) Co/simplicial models for manifold calculus/factorization homology 22 Feb 2pm CYCL08 Don Stanley (U. Regina) 22 Feb - 4 Mar Persistence modules and quivers 26 Feb (Friday) 3pm CYCL08 Hoel Quefellec (U. Montpellier) 26 Feb Catégories de mousses et groupes quantiques catégorifiés 29 Feb 2pm E161 Georgios Raptis (U. Regensburg) 29 Feb - 4 Mar Parametrized homotopy theory and bivariant A-theory 7 Mar 2pm E349 Abdó Roig-Marangues (UPC at Barcelona) 7 - 10 Mar On the homotopy type of spaces of algebraic cycles and cocycles 14 Mar 2pm E161 Julien Ducoulombier (U. Paris 13) 11 - 14 Mar Etude de l'opérade Swiss-Cheese et applications à la théorie des longs noeuds 21 Mar 28 Mar Pâques 4 Apr Pâques 11 Apr 18 Apr 2pm CYCL08 Rosona Eldred (WWU Münster) 18 - 21 Apr Equivalence of models for deRham cohomology of ring spectra 25 Apr 2 May 2pm CYCL08 Zbigniew Blaszczyk (U. Poznan) 1 - 4 May (De)constructing actions on product manifolds with an asymmetric factor 9 May 2pm CYCL08 Urtzi Buijs (U. Málaga) 2 - 31 May Lie models and higher order Whitehead products 16 May Pentecôte 23 May 2pm CYCL05 Federico Cantero Morán (UC Louvain) Rational homotopy theory of Thom spaces 30 May 2pm CYCL08 Paul Arnaud Tsopméné (UC Louvain) Swiss-Cheese algebra structure on the Hochschild homology of long knots and long links 6 June 2pm CYCL08 José Gabriel Carrasquel (UC Louvain) Efficent topological complexity

2015

 5 Feb 2pm CYCL08 Daniel Tubbenhauer (UC Louvain) Uq(sl_n) diagram categories via q-Howe duality 12 Feb 1pm CYCL08 Pascal Lambrechts (UC Louvain) Sur le type d'homotopie rationnel des espaces de configurations dans une variété fermée 19 Feb 2pm CYCL08 Geoffroy Horel (Münster) Profinite completion of operads and the absolute Galois group of Q 25 Feb 2pm CYCL08 Ulrich Bauer (München) Induced Matchings and the Algebraic Stability of Persistence Barcodes 12 Mar 2pm CYCL08 Paul Arnaud Tsopmene (UCL) The rational homology of the space of high string links 19 Mar 2pm CYCL08 Victoria Lebed (Nantes) Braided diagrams as a unifying tool in homology theory 26 Mar 2pm CYCL08 Claudia Scheimbauer (ETH Zurich) Factorization homology as a fully extended topological field theory 1 Apr 12.45pm CYCL08 Yves Felix (UC Louvain) Homotopie rationelle des espaces fonctionnelles 23 Apr 1.30pm CYCL08 Julien Ducoulombier (Paris 13) Etude des totalisations d'une opérade colorée et applications à l'espace des longs noeuds 23 Apr 2.45pm CYCL08 Paul Wedrich (Cambridge) Deformations of link homologies 30 Apr 2pm CYCL08 Krzysztof Putyra (ETH Zurich) The annularization of the Khovanov arc algebras 7 May 2pm CYCL08 Sinan Yalin(Luxembourg) Champs dérivés de structures algébriques 21 May 2pm CYCL08 Victor Turchin(Kansas State) Le type d'homotopie rationelle des delooping des espaces de longs plongements 4 June 11am CYCL08 Martin Palmer(Münster) Homological stability for configuration spaces on closed manifolds 15 June 2pm CYCL08 Josh Sussan(CUNY) Categorical Heisenberg and related structures 9 Sept 11am CYCL08 Matija Basic (Zagreb) Stable homotopy theory of dendroidal sets 14 Oct 2pm CYCL08 Andrea Cesaro (Lille) The divided symmetries preLie algebras 28 Oct 2pm CYCL08 Najib Idrissi (Lille) L'opérade Swiss-Cheese et le centre de Drinfeld 18 Nov 2pm CYCL08 Jonathan Grant (Durham) Skew Howe duality in Type A quantum knot invariants 25 Nov 2pm CYCL08 Ricardo Campos (University of Zurich) A graph model for configuration spaces of points on a manifold

2014

 16 Oct 2pm CYCL04 Pedro Boavida (UC Louvain) Operads and their derived mapping spaces 23 Oct 2pm CYCL08 Pascal Lambrechts (UC Louvain) Cosimplicial model of embedding space 30 Oct 2pm CYCL05 Miradain Atontsa Nguemo (UC Louvain) Categorification of Persistent Homology 6 Nov 2.15pm CYCL08 Federico Cantero (Münster) The stable homology of the space of embedded surfaces in a manifold 13 Nov 2.30pm CYCL05 Muriel Livernet (Paris 13) Non-formality of the Swiss-cheese operad 20 Nov 2pm CYCL08 Daniela Egas Santander (Bonn) Comparing combinatorial Models of the Moduli space of Riemann surfaces 27 Nov 2pm CYCL05 Michael Ehrig (Bonn) Categorification and three dualities: Schur-Weyl, skew Howe, Koszul 4 Dec 2pm CYCL08 Antonio Sartori (Freiburg) gl(1|1), the Alexander polynomial and categorification 9 Dec 9.30am CYCL08 Jose Gabriel Carrasquel Vera(UC Louvain) On the sectional category of certain maps 9 Dec 17.00pm CYCL08 Don Stanley(Univ Regina) Connected sums of quasi-toric manifolds

Abstracts

2016

• Marco Mackaay (U Algarve) Nov 9
The 2-representation theory of Soergel bimodules

2-Representations of monoidal categories and 2-categories are categorical analogues of representations of algebras. Well known examples show up in the context of categorified quantum groups, Category O and Soergel bimodules (the latter giving categorifications of Hecke algebras).
More recently, Mazorchuk and Miemietz have started to develop a theory of 2-representations, in an attempt to study them more systematically. One (difficult) question that naturally arises for any given monoidal category or 2-category (satisfying some technical conditions), is the classification of its “categorical irreducible representations", the so called simple transitive 2-representations.
In a joint paper with Kildetoft, Mazorchuk and Zimmermann and another one with Tubbenhauer, we obtained a complete classification of all simple transitive 2-representations of the so called “small quotient” of the monoidal category of Soergel bimodules, for any finite Coxeter type.
In my talk, I will first explain some of the general ideas in 2-representation theory and then illustrate them by focusing on the 2-representation theory of the monoidal category of Soergel bimodules.

• Pascal Lambrechts (UC Louvain) Feb 15
Co/simplicial models for manifold calculus/factorization homology
Goodwillie-Weiss manifold calculus is a way to approximate contravariant functors from the category of manifolds to topological spaces, in the spirit of Taylor approximation in calculus. In this talk I will explain how to build an explicit cosimplicial model of that approximation out of a simplicial model of the manifold, which leads to an efficient tools for computations. This is a wide generalization of the cosimplicial model of Sinha for long knots. A dual version of this gives a simplicial model for factorization homology. This is joint work with Pedro Boavida, Daniel Pryor and Arnaud Songhafouo.

• Don Stanley (U. Regina) Feb 22
Persistence modules and quivers
Abstract: In classical persistence where we have a sequence of modules indexed by the natural numbers, modules are determined by their barcodes (ie the integers where they start and end), and we can use the barcodes to compute the interleaving distance between modules. In this talk we study persistence modules indexed by a quiver (ie a directed graph) and desribe an interleaving distance using the socles and radicals of the modules. When the quiver is A_n (ie n points with arrows going in one direction between them), we relate this interleaving distance to the classical one. Joint work with Peter Bubenik and Jonathan Scott.

• Hoel Quefellec (U. Montpellier) Feb 26
Catégories de mousses et groupes quantiques catégorifiés
Il y a une quinzaine d'années, Khovanov a introduit un invariant homologique qui catégorie le polynôme de Jones. Bien que ce polynôme s'interprète à la fois en termes de théorie des représentations et en termes diagrammatiques, pendant longtemps seule la seconde version a été catégorifiée. J'expliquerai comment, en utilisant le concept d'antidualité de Howe développé par Cautis, Kamnitzer, Morrison et Licata, on peut décrire les catégories de cobordismes utilisées dans l'homologie de Khovanov à partir des groupes quantiques catégorifiés. En retour, cette méthode nous permet de réinterpréter les généralisations sln des catégories de cobordismes dues à Mackaay-Stosic-Vaz, amenant ainsi une description combinatoire et sur Z des homologies de Khovanov-Rozansky. Travail commun avec Aaron Lauda et David Rose.

• George Raptis (U. Regensburg) Feb 29
Parametrized homotopy theory and bivariant A-theory
Waldhausen's algebraic K-theory of spaces is an extension of algebraic K-theory from rings to spaces or ring spectra, which encodes the stable homotopy type as well as important geometric information of the space. Bivariant A-theory, introduced by B. Williams, is a further extension of algebraic K-theory from spaces to fibrations of spaces. In this talk, I will recall the definition and basic properties of bivariant A-theory and discuss its connection with parametrized homotopy theory. Time permitting, I will also explain how bivariant A-theory enters in the study of the A-theory Euler characteristic and the Dwyer-Weiss-Williams theorems. (Parts of this talk are based on separate joint works with John Lind, and with Wolfgang Steimle.)

• Abdó Roig-Marangues (UPC at Barcelona) Mar 7
On the homotopy type of spaces of algebraic cycles and cocycles
I will talk about the Friedlander-Lawson approach of studying algebraic cycles on a complex variety $X$, in which the homotopy type of the moduli space of such cycles is regarded as a geometric invariant of $X$ of motivic nature. These invariants are realized by very explicit and geometric spaces which may be susceptible to geometric or analytic techniques, not available to more algebraic or top-down approach to motivic cohomology. In the first part I'll introduce the theory, and describe some computations for singular varieties toric varieties. Finally, I'll discuss some future directions and open problems.

• Julien Ducoulombier (U. Paris 13) Mar 14
Etude de l'opérade Swiss-Cheese et applications à la théorie des longs noeuds
L'objectif est l'étude de l'opérade Swiss-Cheese qui est une version relative de l'opérade des petits cubes. On montre que les théorèmes classiques dans le cadre des opérades non colorées admettent des analogues dans le cas relatif. Il est possible d'extraire d'un morphisme opérades colorée un couple d'espaces induisant une algèbre sous l'opérade Swiss-Cheese en dimension 1. En admettant la conjecture de Dwyer-Hess, il est alors possible d'identifier des algèbres sous l'opérades Swiss-Cheese en dimension d+1. Ainsi il possible d'identifier le couple (espace des longs noeuds en dimension supérieure ; tour de goodwillie associé aux (k)-immersions) à une algèbre sous l'opérades Swiss-Cheese en dimension d+1.

• Rosona Eldred (WWU Münster) Apr 18
Equivalence of models for deRham cohomology of ring spectra
The HKR theorem gives us an important equivalece between the Hochschild homology groups and the groups in the chain complex used to calculate deRham cohomology, for (rational) commutative differential graded algebras. Kantorovitz-McCarthy realized this as a statement about the layers of the Taylor tower of a certain functor. In joint work with Bauer, Johnson and McCarthy¸we use the recently developed unbased calculus to promote this to a statement for ring spectra, conjectured originally by Waldhausen, and show it is equivalent to another proposed combinatorial model.

• Zbigniew Blaszczyk (U. Poznan) May 2
(De)constructing actions on product manifolds with an asymmetric factor
I will discuss transformation groups of manifolds of the form $M \times S^n$, where $M$ is an asymmetric manifold, i.e. it does not admit any non-trivial action of a compact group. The starting point is the following question: $M \times S^n$ is clearly not asymmetric, but does it admit non-diagonal actions? We will see that the answer typically is “yes”; in fact, provided that $n \geq 2$, there exist infinitely many distinct non-diagonal effective circle actions on such products, and a similar result holds for cyclic groups of prime order. On the other hand, if $M$ is one of the “almost asymmetric” manifolds considered previously by V. Puppe and M. Kreck, then every free circle action on $M \times S^1$ turns out to be equivalent to a diagonal one. The talk is based on joint work with M. Kaluba.

• Urtzi Buijs (U. Malaga) May 9
Lie models and higher order Whitehead products
We study higher order Whitehead products on the homology H of a differential graded Lie algebra L in terms of higher brackets in the transferred L-infinity structure on H via a given homotopy retraction of L onto H.

• Federico Cantero Morán(UCL) May 23
Rational homotopy theory of Thom spaces
Thom spaces of vector bundles are fundamental objects in algebraic topology which arise as the target of Pontryagin-Thom constructions. Nonetheless, their rational homotopy type has only been studied in the most interesting cases: when the base space of the vector bundle is the classifying space of a group (Papadima, 1985). In this talk we will address this problem for a general base. This is work in progress with Urtzi Buijs.

• Paul Arnaud Tsopméné UCL) May 30
Swiss-Cheese algebra structure on the Hochschild homology of long knots and long links
Let K (respectively MV) be the Sinha cosimplicial model for the space of long knots (respectively the Munson-Volic cosimplicial model for the space of long links). The goal of this talk is to show that the pair (HH(K), HH(MV)) formed by the Hochschild homology of K and MV is endowed with a natural Swiss-Cheese algebra structure. This is a joint work with Julien Ducoulombier.

• José Gabriel Carrasquel Vera (UCL) June 6
Efficent topological complexity
We introduce a variant of topological complexity, defined for compact Riemannian manifolds, which takes into account the notion of efficiency in terms of total covered distance. We prove that it can be approximated by classical topological complexity. Joint work with Z. Blaszczyk

• 2015

 Daniel Tubbenhauer (UC Louvain)Uq(sl_n) diagram categories via q-Howe duality The "moral, philosophical goal" of this talk is to illustrate that diagrammatic algebra is a rigorous, yet extremely fun, way to attack various problems from algebra, topology and combinatorics (and other things as well). The Temperley-Lieb algebra T Ld is the mother of all diagram algebras. It was introduced by Temperley and Lieb in the 70ties in their study of statistical mechanics. Also due to its simple presentation, it reappears nowadays in low dimensional topology, operator theory, algebraic combinatorics and Lie theory (to name a few). It has its origin in the study of sl2-modules: Rumer, Teller and Weyl showed (more or less) already in the 30ties that T Ld can be seen as a diagrammatic realization of the representation category of sl2-modules - providing a topological tool to study the latter. The "real-life goal" of this talk is to explain how on can show such a realization and discuss some fancy cousins of T Ld, e.g. representation category of sln-modules. Although diagrammatic algebra is one building block of what is called "categorification": do not fear, I will stay in the uncategorified world in this talk. Pascal Lambrechts (UC Louvain)Sur le type d'homotopie rationnel des espaces de configurations dans une variété fermée Soit M une variété fermée et Conf(M,k) l'espace des configurations ordonnées de k points distincts dans M. Nous démontrons que, pour M 4-connexe, le type d'homotopie rationnel de Conf(M,3) ne dépend que du type d'homotopie rationnel de M et admet un modèle explicite simple exprimé à partir d'un modèle à dualité de Poincaré de M. Ils semble que la preuve se généralise à tout k>=3. Geoffroy Horel (Münster)Profinite completion of operads and the absolute Galois group of Q Abstract: I will first talk about the profinite completion of spaces. This is a construction originally due to Artin and Mazur which approximates a space by truncated spaces with finite homotopy groups. One can then talk about the profinite completion of operads in spaces. It turns out that the profinite completion of the operad of little 2 dimensional disks has a faithful action of the absolute Galois group of Q. To conclude, I will try to sketch a conceptual argument explaining this action using the theory of the étale homotopy type. Ulrich Bauer (München)Induced Matchings and the Algebraic Stability of Persistence Barcodes Abstract: We define a simple, explicit map sending a morphism f : M -> N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f. As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes, a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a Å’Â¥-interleaving morphism between two persistence modules induces a Å’Â¥-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Paul Arnaud Tsopmene (UCL)he rational homology of the space of high string links Abstract: (Joint work with Victor Turchin) Let L be the high dimensional analogues of the space of string links. We will show that the rational homology of L can be expressed in terms of derived morphisms of some right modules over the category of finite sets and surjections. Our approach is mainly based on a version, developed by Arone and Turchin, of the Goodwillie-Weiss embedding calculus. If time permits, I will say something about the Hodge decomposition of the homology of L. Victoria Lebed (Nantes)Braided diagrams as a unifying tool in homology theory Abstract: Diagrammatic calculus has the reputation of a powerful and easy-to-manipulate tool applicable to categories, quantum group representations, operads, categorification constructions, and numerous other mathematical contexts. In this talk a particular "braided" type of diagrams will appear in a new and quite unexpected setting - namely, as a unifying tool for different homology theories (among others, Hochschild homology of associative algebras, Gerstenhaber-Schack homology of bialgebras, Chevalley-Eilenberg homology of Lie algebras, various homology theories of self-distributive structures). Knot- and braid-theoretic applications of our constructions will be presented. Claudia Scheimbauer (ETH Zurich)Factorization homology as a fully extended topological field theory Abstract: (Homotopy) algebras and (pointed) bimodules over them can be viewed as factorization algebras on the real line R which are locally constant with respect to a certain stratification. Moreover, Lurie proved that E_n-algebras are equivalent to locally constant factorization algebras on R^n. Starting from these two facts I will explain how to model the Morita category of E_n-algebras as an (\infty, n)-category. Every object in this category, i.e. any E_n-algebra A, is "fully dualizable" and thus gives rise to a fully extended TFT by the cobordism hypothesis of Baez-Dolan-Lurie. I will explain how this TFT can be explicitly constructed by (essentially) taking factorization homology with coefficients in the E_n-algebra A. Julien Ducoulombier (Paris 13) Etude des totalisations d'une opérade colorée et applications à l'espace des longs noeuds Abstract: McClure et Smith ont démontré que si un espace cosimplicial provenait d'une opérade multiplicative alors sa totalisation homotopique avait le type d'homotopie d'un espace de lacet double. La principale application concerne l'espace des longs noeuds qui peut s'exprimer comme la totalisation homotopique de l'operade de Kontsevich. Cependant, d'autres espaces (comme les entrelacs ou les k-immersions) peuvent juste s'exprimer comme la totalisation homotopique d'un bimodule sous l'operade de Kontsevich. On peut les écrire comme un espace de lacets mais on perd l'information provenant de l'opérade. Le but de cet exposé est de montrer comment récupérer cette information. Pour cela on va utiliser l'opérade Swiss-Cheese (SC) qui est une version relative de l'opérade des petits disques. On va démontrer que si un couple d'espaces cosimpliciaux provient d'une opérade colorée alors il est faiblement équivalent à un SC-espace. On appliquera ces résultats aux couples: 1- (Longs Noeuds ; entrelacs) 2- (Longs noeuds ; k-immersions) Paul Wedrich (Cambridge)Deformations of link homologies Abstract: I will start by explaining how deformations help to answer two important questions about the family of (colored) sl(N) link homology theories: What relations exist between them? What geometric information about links do they contain? I will recall Bar-Natan and Morrison's version of Lee's deformation of Khovanov homology and sketch how it generalizes to the case of colored sl(N) link homology. Finally, I will state a decomposition theorem for deformed colored sl(N) link homologies which leads to new spectral sequences between various type A link homologies and concordance invariants in the spirit of Rasmussen's s-invariant. Joint work with David Rose. Krzysztof Putyra (ETH Zurich)The annularization of the Khovanov arc algebras Abstract: Given a monoidal category one defines its annularization by considering it as a 2-category with a single object and taking its horizontal trace. For instance, the annularization of a Temperley-Lieb category is the category of points on a circle and flat tangles in an annulus. In my talk I will construct the annularization of the Khovanov's monoidal 2-category of bimodules over algebras $H^n$. This new 2-category produces an invariant of annular tangles, which in the case of links matches the degree zero piece of the annular Khovanov homology. This is a joint work with A. Beliakova Sinan Yalin (Luxembourg)Champs dérivés de structures algébriques Abstract: Je commencerai par expliquer comment les props paramètrent diverses structures de bigèbres. Les résolutions de ces props définissent des structures algébriques à homotopie près, qui apparaissent dans divers contextes en topologie et géométrie. J'expliquerai qu'une telle définition ne dépend pas, à homotopie près, du choix d'une résolution. Une idée pertinente pour comprendre le comportement de telles structures est de les étudier comme un problème de moduli. Pour cela, je définirai la notion d'espace de modules simplicial de structures algébriques, et montrerai comment de tels espaces de modules s'interprètent dans le cadre de la géométrie algébrique dérivée au sens de Toen-Vezzosi. Victor Turchin (Kansas State) Le type d'homotopie rationelle des delooping des espaces de longs plongements Abstract: On décrit le type d'homotopie rationelle de l'espace de morphismes d'opérades Operad(B_m,B_n), n-m>2, comme un complexe des graphes à cheveux muni d'une structure de dg algèbre de Lie (L_\infty dans le cas m=1). Martin Palmer (Münster)Homological stability for configuration spaces on closed manifolds Abstract: Unordered configuration spaces of points (or particles) on connected manifolds are basic objects that appear in connection with many different areas within topology. When the manifold M is non-compact, a theorem of McDuff and Segal states that these spaces satisfy a phenomenon known as homological stability: fixing q, the homology groups H_q(C_k(M)) are eventually independent of k. Here, C_k(M) denotes the space of k-point configurations and homology is taken with coefficients in Z. On the other hand, this statement is generally false for closed manifolds M, although some conditional results in this direction are known. I will explain some recent joint work with Federico Cantero, in which we extend the previously known results in this situation. A key idea is to introduce so-called "replication maps" between configuration spaces, which in a sense replace the "stabilisation maps" that exist only in the case of non-compact manifolds. One corollary of our results is to recover a "homological periodicity" theorem of R. Nagpal -- taking homology with field coefficients and fixing q, the sequence of homology groups H_q(C_k(M)) is eventually periodic in k -- and we obtain a much simpler estimate for the period. Another result is that homological stability holds with Z[1/2] coefficients whenever M is odd-dimensional, and we improve this to stability with Z coefficients for 3- and 7-dimensional manifolds. Josh Sussan (CUNY)Categorical Heisenberg and related structures Abstract: A graphical category whose Grothendieck group contains a Heisenberg algebra was constructed by Khovanov. By considering certain complexes in the corresponding homotopy category we obtain a conjectural boson-fermion correspondence on the level of categories. We will also study a super version of Khovanov's category in order to obtain a twisted Heisenberg algebra. Matija Basic (Zagreb)Stable homotopy theory of dendroidal sets Abstract: Dendroidal sets are a generalization of simplicial sets. They are devised to serve as combinatorial models for algebraic structures up to (coherent) homotopy. In this talk we will first recall the basic definitions of the theory of dendroidal sets. Next, we will give an overview of homotopy theories showing that dendroidal sets are models both for topological operads and for connective spectra. Towards the end we will discuss the relation to connective spectra in more detail, as well as a homology theory of dendroidal sets that makes this relation more explicit. Andrea Cesaro (Lille)The divided symmetries preLie algebras Abstract: The structure of preLie algebra naturally appears in many different domains of mathematics, in special way in the deformation theory of algebraic structures. The aim of this talk will be to explain the constructions of divided powers structures, \Lambda(PreLie,-) and \Gamma(PreLie,-)-algebras, associated to preLie algebras and their applications. The definition of these divided powers structures is based on the notion of divided symmetries algebras introduced by B.Fresse in the context of operads to generalize a result of H. Cartan on the homotopy of commutative simplicial algebras. We will show that the \Lambda(PreLie,-)-algebras are identified with the restricted preLie algebras introduced by A. Dzhumadil'daev and we will give an explicit description of \Gamma(PreLie,-)-algebras in terms of brace-type operations. Najib Idrissi (Lille)Lâ€™opérade Swiss-Cheese et le centre de Drinfeld Abstract: L'opérade SC "Swiss-Cheese" de Voronov gouverne l'action d'une algèbre D_2 sur une algèbre D_1, où D_n est l'opérade des petits n-disques. Dans cet exposé, j'expliquerai comment obtenir une opérade faiblement équivalente au groupoide fondamental de SC : un premier modèle en groupoides qui fait intervenir le centre de Drinfeld des catégories monoidales, et un second modèle rationel qui utilise un associateur de Drinfeld. On comparera ce second modèle Ã  l'opérade déduite de l'homologie H(SC), la différence étant expliquée par la non-formalité de SC. Jonathan Grant (Durham)Skew Howe duality in Type A quantum knot invariants Abstract: Both the Jones polynomial and the Alexander polynomial can be viewed as invariants arising from the representations of quantum (super)groups in type A. Skew Howe duality give these invariants particularly nice descriptions in terms of trivalent diagrams. This method is particularly powerful when defining knot homology theories categorifying these polynomials. I will discuss the relationship between representations of quantum groups and the trivalent diagrams appearing in calculations of knot invariants, and describe how this can be used to understand knot homology theories, and progress towards obtaining a 'quantum' categorification of the Alexander polynomial. Ricardo Campos (University of Zurich)A graph model for configuration spaces of points on a manifold Abstract: Given a closed oriented manifold M, one can study the configuration space of n points on the manifold, which is the subspace of M^n in which two points cannot be in the same position. The study of these spaces is of interest in areas such as algebraic topology, rational homotopy theory or quantum field theory. Despite the apparent simplicity, even the homology of these spaces is reasonably unknown. In this talk, assuming that the manifold is parallelized and using an operadic approach I plan to exhibit a simpler chain complex of graphs that is quasi-isomorphic to the chains of the configuration space of points and compatible with some additional structure. The general 2 dimensional case will also be discussed. This is a joint work in progress with Thomas Willwacher.

2014

 Pedro Boavida (UC Louvain)Operads and their derived mapping spaces Abstract: I will discuss a weakening, due to Cisinski-Moerdijk, of the notion of an operad and indicate how it can be used to understand/compute derived mapping spaces of operads. As an application, I will present a geometrically flavoured description (joint work with Michael Weiss) of the derived space of maps from the little n-discs operad to the little m-discs operad in terms of the so-called configuration categories. This has implications for spaces of smooth embeddings and for (certain quotients of) the space of homeomorphisms of R^n. Pascal Lambrechts (UC Louvain)Cosimplicial model of embedding space Abstract: In a former work with Arone and Pryor that I will recap, we proved that the rational homology of the space of embeddings of a manifold M in a euclidean space, Emb(M,R^d), has an exponential growth. This result was a consequence of the existence of a small *rational* cosimplicial model of Emb(M,R^d) directly constructed from a simplicial model of the manifold M and configuration spaces. The proof of existence of this rational cosimplicial model relied a lot on Kontsevich's formality of the little disk operad. In a work in progress with Pryor and Songhafouo we construct an *integral* cosimplicial model of Emb(M,R^d) again by applying configuration space to a simplical model of the manifold, which is sort of an embedding analog of the classical Andersen's cosimplicial model of a mapping space map(X,Y) built out of a simplicial model of the source X. Miradain Atontsa Nguemo (UC Louvain)Categorification of Persistent Homology Abstract: Algebraic topology offers many tools for counting and collating holes and other topological features in spaces and maps between them. In may situations, even our usual projection process to visualise high-dimensional data doesn't reveal certain topological features (e.g telescope image, images with noises,â€šÃ„Â¶). From point cloud data (finite subset of a Euclidean n-dimensional space E), we can construct many parameterized(on Z, N, or R) complexes such as the Cech complex, the Rips complex, the Morse complex, etc. However, the computation of such complexes at a particular parameter is generally insufficient in term of revealing topological features of the space(e.g:manifolds,...) where the point cloud data has been extracted. One requires a means of declaring which holes are true on the space and which ones are noise. Persistence, as introduced by Edelsbrunner, Letscher, and Zomorodian in 2002, and refined later in 2005 by Carlsson and Zomorodian is a rigorous response to this issue. That is, given a parameterized family of spaces, those topological features which persists over a significant parameter range are to be considered as signal, and with short-lived features as noise. Our objective through this talk is to firstly make a short state of art on this new tool, and then present a categorification approach of persistent homology introduced by Peter Bubenik and Jonathan Scott in 2012. Federico Cantero (Münster)The stable homology of the space of embedded surfaces in a manifold Abstract: The Madsen--Weiss theorem identifies the homology of the moduli space of oriented compact connected surfaces of genus $g$ in the homological range $*\leq \frac{2}{3}(g-1)$ with the homology of certain infinite loop space. In this talk we will present the analogous theorem for the moduli space of oriented compact connected subsurfaces of a fixed background manifold. This is joint work with Oscar Randal-Williams. Muriel Livernet (Paris 13)Non-formality of the Swiss-cheese operad Abstract: I will review in this talk the notion of formality for operads and some classical results. I will then intoduce the Swiss-cheese operad and explain the differences between the Swiss-cheese operad and the little disk operad. Finally I will prove the non-formality of the Swiss-cheese operad. Daniela Egas Santander (Bonn)Comparing combinatorial Models of the Moduli space of Riemann surfaces Abstract: I will compare two combinatorial models of the Moduli space of two dimensional cobordisms. More precisely, I will construct direct connections between the space of metric admissible fat graphs due to Godin and the chain complex of black and white graphs due to Costello. Furthermore, I will construct a PROP structure on admissible fat graphs, which models the PROP of Moduli spaces of two dimensional cobordisms. I will use the connections above to give black and white graphs a PROP structure with the same property. If time permits, I will mention how Bödigheimer's model of radial slit configurations fit into this picture; and how this shows that the space of Sullivan diagrams, is homotopy equivalent to Bödigheimer's Harmonic compactification of Moduli space. Michael Ehrig (Bonn)Categorification and three dualities: Schur-Weyl, skew Howe, Koszul Abstract: In the talk I will relate classical dualities, like Schur-Weyl or skew Howe duality, to categorification methods, both in already known cases as well as new ones. The BGG category O and generalizations of Khovanov's arc algebra play an important role here. This is joint work with Catharina Stroppel. Antonio Sartori (Freiburg)gl(1|1), the Alexander polynomial and categorification Abstract: Intertwining operators of Lie algebra representations can be used to define link invariants, like the Jones polynomial, and their categorifications provide link homology theories, like Khovanov Homology. In the talk, I will consider the analogous case of the Lie superalgebra gl(1|1). I will explain how the Alexander polynomial can be constructed using its representation theory, and I will present an approach to its categorification which points towards a link homology theory for the Alexander polynomial. Jose Gabriel Carrasquel Vera (UC Louvain)On the sectional category of certain maps Abstract: We give a simple characterisation of the sectional category of rational maps admitting a homotopy retraction which generalises the Félix-Halperin theorem for rational LS category. As a particular case, we prove a conjecture of Jessup-Murillo-Parent concerning rational topological complexity and generalise it to Rudyak's higher topological complexity. Don Stanley (Regina)Connected sums of quasi-toric manifolds Abstract: A quasi-toric manifold is topological version of a toric variety. It can be constructed out of a simple convex polytope together with some vectors assigned to each facet. This combinatorial data determines the manifold, and there are direct formulas which describe the cohomology. These manifold also have natural torus actions. We look at what happens when we take a connected sum of two such manifolds along orbits of this torus action. In particular we compute the rational cohomology.