BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Richard Garner (Macquarie University) DTSTART:20200811T001500Z DTEND:20200811T011500Z DTSTAMP:20260404T094507Z UID:operad/1 DESCRIPTION:Title: Sweedler duals for monads\nby Richard Garner (Macquarie Universi ty) as part of operad pop-up\n\n\nAbstract\nWhile the linear dual of any c oalgebra is an algebra\, the converse is not true\; however\, there is an adjoint to the coalgebra-to-algebra functor\, given by the so-called Sweed ler dual.\n\nThere is a notion of “linear dual” for an endofunctor of Set\, given by homming into the identity functor for the Day convolution s tructure. Again\, this sends comonads to monads\, but not vice versa\; but again\, there is an adjoint. This “Sweedler dual” comonad of a monad was introduced by Katsumata\, Rivas and Uustalu in 2019.\n\nThe purpose of this talk is to give an explicit construction of the Sweedler dual comona d of any monad on Set. The category of coalgebras for the Sweedler dual tu rns out to be a presheaf category\, whose indexing category can be describ ed explicitly in terms of a kind of computational dynamics of the monad. I f time permits\, we also describe the source-etale topological category wh ich classifies the topological Sweedler dual comonad of a monad on Set\; i n particular\, this recovers all kinds of etale topological groupoids of i nterest in the study of combinatorial $C^*$-algebras.\n LOCATION:https://stable.researchseminars.org/talk/operad/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophie Raynor (Macquarie University) DTSTART:20200811T030000Z DTEND:20200811T040000Z DTSTAMP:20260404T094507Z UID:operad/2 DESCRIPTION:Title: Unpacking the combinatorics of modular operads\nby Sophie Raynor (Macquarie University) as part of operad pop-up\n\n\nAbstract\nWhilst ope rads are governed by trees\, undirected graphs of arbitrary genus are need ed in order to describe modular operads. And this can get complicated. Esp ecially if we're interested in understanding notions of modular operads\, such as Joyal and Kock's compact symmetric multicategories\, where the combination of the contraction operation and a unital operadic composi tion presents particular challenges.\n\nI'll describe how to first break t he problem into its constituent parts\, and then use the classical theory of distributive laws to put the pieces back together. The decomposition al lows us to apply Weber's theory to get a fully faithful nerve via complete ly abstract methods. More interestingly\, the proof method makes the combi natorics of modular operads\, and especially the fiddly stuff\, completely explicit. Hence it provides a roadmap for developing the theory\, and the possibility for gaining new conceptual insights into the structures descr ibed.\n LOCATION:https://stable.researchseminars.org/talk/operad/2/ END:VEVENT BEGIN:VEVENT SUMMARY:María Ronco (Universidad de Talca) DTSTART:20200811T213000Z DTEND:20200811T223000Z DTSTAMP:20260404T094507Z UID:operad/3 DESCRIPTION:Title: Order and substitution on graph associahedra\nby María Ronco (U niversidad de Talca) as part of operad pop-up\n\n\nAbstract\nM. Carr and S . Devadoss introduced in [1] associated a finite partially ordered set to any simple finite graph\, whose geometric realization is a convex polytope ${\\mathcal K}\\Gamma$\, the graph-associahedron. Their construction incl ude many well-known families of polytopes\, liked permutahedra\, associahe dra\, cyclohedra and the standard simplexes.\n\nThe goal of the present wo rk is to give an algebraic description of graph associahedra. We in troduce a substitution operation on Carr and Devadoss tubings\, which allo ws us to describe graph associahedra as a free object on the set of all co nnected simple graphs\, for a type of colored operad generated by pairs of a finite connected graph and a connected subgraph of it.\n\nWe show that substitution of tubings may be understood in the context of M. Batanin and M. Markl's operadic categories. We describe an order on the faces of grap h-associahedra\, different from the one given by Carr and Devadoss\, which allows us to construct a standard triangulation of graph associahedra\, f ollowing [2].\n\n(joint work with Stefan Forcey)\n\n[1] M. Carr\, S. Devad oss\, Coxeter complexes and graph associahedra\, Topol. and its App lic. 153 (1-2) (2006) 2155–2168.
\n[2] J.-L. Loday\, Parking fun ctions and triangulation of the associahedron\, Proceedings of the Str eet’s fest 2006\, Contemp. Math. AMS 431 (2007)\, 327–340.\n LOCATION:https://stable.researchseminars.org/talk/operad/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Ching (Amherst College) DTSTART:20200811T184500Z DTEND:20200811T194500Z DTSTAMP:20260404T094507Z UID:operad/4 DESCRIPTION:Title: Goodwillie calculus and operads\nby Michael Ching (Amherst Colle ge) as part of operad pop-up\n\n\nAbstract\nThe goal of this talk is to su rvey the role of operads in Goodwillie’s calculus of functors. A key obs ervation is that the derivatives of the identity functor\, on a suitable p ointed $\\infty$-category $C$\, admit an operad structure which in the cas e of pointed spaces recovers a spectral version of the Lie operad. I will give a couple different ways to construct the operad structure in general\ , and then focus on the case where $C$ is itself the $\\infty$-category of algebras over some (stable\, non-unital) operad $P$. In that case\, the d erivatives of the identity functor on $C$ recover\, in some form\, the ope rad $P$.\n LOCATION:https://stable.researchseminars.org/talk/operad/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Syunji Moriya (Osaka Prefecture University) DTSTART:20200811T041500Z DTEND:20200811T051500Z DTSTAMP:20260404T094507Z UID:operad/5 DESCRIPTION:Title: A spectral sequence for cohomology of knot spaces\nby Syunji Mor iya (Osaka Prefecture University) as part of operad pop-up\n\n\nAbstract\n This talk is based on the preprint arXiv:2003.03815.\nLet $Emb(S^1\,M)$ be the space of embeddings from $S^1$ to a closed manifold $M$ (space of kno ts in $M$). Recently\, this space is studied by Arone-Szymik\, Budney-Gaba i\, and Kupers\, using Goodwillie-Weiss embedding calculus. In this talk\, we introduce a spectral sequence for cohomology of $Emb(S^1\,M)$ whose $E _2$-term has an algebraic presentation\, using Sinha's cosimplicial model which is derived from the calculus. This converges to the correct target i f $M$ is simply connected and of dimension $\\geq 4$ for general coeffici ent ring. Using this\, we see a computation of $H^*(Emb(S^1\,S^k\\times S ^l))$ in low degrees under some assumption on $k\,l$ and an isomorphism \n $\\pi_1(Emb(S^1\,M))\\cong H_2(M\,\\mathbb{Z})$ for some simply connected $4$-dimensional $M$. \n\nOur main idea of the construction is to replace configuration spaces in the cosimplicial model with fat diagonals via P oincaré Lefschetz duality. To do this\, we use a notion of a (co)module o ver an operad. A somewhat curious point is that we need spectra (in stable homotopy) even though our concern is singular cohomology.\n LOCATION:https://stable.researchseminars.org/talk/operad/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Petersen (Stockholms universitet) DTSTART:20200811T090000Z DTEND:20200811T100000Z DTSTAMP:20260404T094507Z UID:operad/6 DESCRIPTION:Title: Lie\, associative and commutative quasi-isomorphism\nby Dan Pete rsen (Stockholms universitet) as part of operad pop-up\n\n\nAbstract\nLet A and A' be commutative dg algebras over Q. There are two a priori differe nt notions of what it means for them to be quasi-isomorphic: one could ask for a zig-zag of quasi-isomorphisms in the category of commutative dg alg ebras\, or a zig-zag in the larger category of not necessarily commutative dg algebras. Our first main result is that these two notions coincide. Th e second main result is Koszul dual to the first\, and states that if two dg Lie algebras over Q have quasi-isomorphic universal enveloping algebras \, then the derived completions of the two dg Lie algebras are quasi-isomo rphic. The latter result is new even for classical Lie algebras concentrat ed in degree zero. Both results have immediate consequences in rational ho motopy theory. (Joint with Campos\, Robert-Nicoud\, Wierstra)\n LOCATION:https://stable.researchseminars.org/talk/operad/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Luciana Basualdo Bonatto (University of Oxford) DTSTART:20200811T101500Z DTEND:20200811T111500Z DTSTAMP:20260404T094507Z UID:operad/7 DESCRIPTION:Title: An infinity operad of normalized cacti\nby Luciana Basualdo Bona tto (University of Oxford) as part of operad pop-up\n\n\nAbstract\nNormali zed cacti are a graphical model for the moduli space of genus 0 oriented s urfaces. They are endowed with a composition that corresponds to glueing s urfaces along their boundaries\, but this composition is not associative. By introducing a new topological operad of bracketed trees\, we show that this operation is associative up-to all higher homotopies and that normali zed cacti form an $\\infty$-operad in the form of a dendroidal space satis fying a weak Segal condition. In particular\, this provides one of the few examples in the literature of infinity operads that are not a nerve of an actual operad.\n LOCATION:https://stable.researchseminars.org/talk/operad/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Joost Nuiten (Université de Montpellier) DTSTART:20200811T114500Z DTEND:20200811T124500Z DTSTAMP:20260404T094507Z UID:operad/8 DESCRIPTION:Title: Moduli problems for operadic algebras\nby Joost Nuiten (Universi té de Montpellier) as part of operad pop-up\n\n\nAbstract\nA classical pr inciple in deformation theory asserts that any formal deformation problem over a field of characteristic zero is classified by a differential graded Lie algebra. This principle has been described more precisely by Lurie an d Pridham\, who establish an equivalence between dg-Lie algebras and forma l moduli problems indexed by Artin commutative dg-algebras. I will discuss an extension of this result to more general pairs of Koszul dual operads over a field of characteristic zero. For example\, there is an equivalence of infinity-categories between pre-Lie algebras and formal moduli problem s indexed by permutative algebras. Under this equivalence\, permutative de formations of a trivial algebra are classified by the usual pre-Lie struct ure on its deformation complex. In the case of the coloured operad for non unital operads\, a relative version of Koszul duality yields an equivalenc e between nonunital operads and certain kinds of operadic formal moduli pr oblems. This is joint work with D. Calaque and R. Campos.\n LOCATION:https://stable.researchseminars.org/talk/operad/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Vallette (Université Sorbonne Paris Nord) DTSTART:20200811T130000Z DTEND:20200811T140000Z DTSTAMP:20260404T094507Z UID:operad/9 DESCRIPTION:Title: Deformation theory of cohomological field theories\nby Bruno Val lette (Université Sorbonne Paris Nord) as part of operad pop-up\n\n\nAbst ract\nI will explain how to develop the deformation theory of cohomologica l field theories as a special case of a general deformation theory of morp hisms of modular operads. Two cases will be considered: a classical and a quantum one. Using ideas of Merkulov–Willwacher based on graphs complexe s\, I will introduce and develop a new universal deformation group which a cts functorially via explicit formulas on the moduli spaces of gauge equiv alence classes of morphisms of modular operads. In the classical case\, th e action is trivial\; but in the quantum case\, this group contains the pr ounipotent Grothendieck–Teichmüller group and its action is highly non- trivial even in the simplest case. Then\, I will enrich these graph comple xes with characteristic classes coming from the geometry of the moduli spa ces of curves and obtain in this way (rather surprisingly) a natural homot opy extension to Givental group action in the classical case\, and in the quantum case\, a huge group that includes both Givental and Grothendieck –Teichmüller groups. \n\nIt is a joint work with Volodya Dotsenko\, Ser gey Shadrin\, and Arkady Vaintrob (arXiv:2006.01649).\n LOCATION:https://stable.researchseminars.org/talk/operad/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathaniel Bottman (University of Southern California) DTSTART:20200811T200000Z DTEND:20200811T210000Z DTSTAMP:20260404T094507Z UID:operad/10 DESCRIPTION:Title: The relative 2-operad of 2-associahedra in symplectic geometry\ nby Nathaniel Bottman (University of Southern California) as part of opera d pop-up\n\n\nAbstract\nThe Fukaya A-infinity category $\\mathrm{Fuk}(M)$ is a rich invariant of a symplectic manifold $M$\, and its manipulation an d computation is a core focus of current symplectic geometry. Building on work of Wehrheim and Woodward\, I have proposed that the correct way to en code the functoriality properties of $\\mathrm{Fuk}$ is by defining an "$( A_\\infty\,2)$-category" called Symp\, in which the objects are symplectic manifolds and hom($M\,N$) is defined to be $\\mathrm{Fuk}(M^-\\times N)$. Underlying the new notion of an $(A_\\infty\,2)$-category is a family of abstract polytopes called 2-associahedra\, which form a "relative 2-operad " (another new notion\, which is related to Batanin's theory of higher ope rads). I will describe all of these constructions from scratch\, without a ssuming any knowledge of symplectic geometry. This talk is based partly on joint work with Shachar Carmeli\, and I will mention related joint work w ith Alexei Oblomkov.\n LOCATION:https://stable.researchseminars.org/talk/operad/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Vaintrob (University of California\, Berkeley) DTSTART:20200811T224500Z DTEND:20200811T234500Z DTSTAMP:20260404T094507Z UID:operad/11 DESCRIPTION:Title: The operad of framed formal curves and a program of Kontsevich\ nby Dmitry Vaintrob (University of California\, Berkeley) as part of opera d pop-up\n\n\nAbstract\nIt has long been conjectured (originally formalize d by Kontsevich) that the operad of framed little disks can be enriched to an operad in an appropriate category of motives (in the sense of Grothend ieck and Voevodsky). I will explain such a construction\, in a motivic cat egory associated to logarithmic schemes (or more generally\, stratified fo rmal schemes) and explain how (via ideas of Kontsevich\, Tamarkin\, Beilin son and others)\, this construction leads to a systematic resolution of se veral formality and deformation theoretic results\, including the Deligne formality conjecture and deformation-quantization previously proven via mo re transcendental techniques.\n LOCATION:https://stable.researchseminars.org/talk/operad/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Cepek (IBS Center for Geometry and Physics) DTSTART:20200811T013000Z DTEND:20200811T023000Z DTSTAMP:20260404T094507Z UID:operad/12 DESCRIPTION:Title: Configuration spaces of $\\mathbb{R}^n$ and Joyal’s category $\\m athbf{\\Theta}_n$\nby Anna Cepek (IBS Center for Geometry and Physics) as part of operad pop-up\n\n\nAbstract\nWe examine configurations of fini te subsets of Euclidean space within the homotopy-theoretic context of $\\ infty$-categories by way of stratified spaces. Through these higher catego rical means\, we identify the homotopy types of these configuration spaces in terms of the category $\\mathbf{\\Theta}_n$.\n LOCATION:https://stable.researchseminars.org/talk/operad/12/ END:VEVENT END:VCALENDAR