BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Katharine Adamyk (University of Western Ontario) DTSTART:20201007T173000Z DTEND:20201007T183000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/1 DESCRIPTION:Title: Classifying stable modules over A(1)\nby Katharine Adamyk (Univ ersity of Western Ontario) as part of University of Regina topology semina r\n\n\nAbstract\nThis talk will present a classification theorem for a cer tain class of modules over A(1)\, a subalgebra of the mod-2 Steenrod algeb ra. In order to give the module classification\, there will be some backgr ound on Margolis homology (an invariant of modules over the Steenrod algeb ra) and the stable module category. Applications of the classification the orem to lifting A(1)-modules to modules over the Steenrod algebra and appl ications to the computation of certain localized Adams spectral sequences will also be discussed.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu Zhang (Nankai University) DTSTART:20201104T223000Z DTEND:20201104T233000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/2 DESCRIPTION:Title: Koszul duality and TQ-homological Whitehead theorem of structured r ing spectra\nby Yu Zhang (Nankai University) as part of University of Regina topology seminar\n\n\nAbstract\nQuillen's work on rational homotopy theory illustrates the duality between differential graded Lie algebras a nd differential graded cocommutative coalgebras. In homotopy theory\, ther e is an analogous duality phenomenon\, called Koszul duality\, where the r ole of differential graded algebras is played by structured ring spectra. In this talk\, I will talk about Koszul duality as well as some of my rela ted recent work on Topological Quillen (TQ) localization and the homologic al Whitehead theorem of structured ring spectra. This is joint with John E . Harper.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Duncan Clark (Ohio State University) DTSTART:20210121T223000Z DTEND:20210121T233000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/3 DESCRIPTION:Title: An intrinsic operad structure for the derivatives of the identity\nby Duncan Clark (Ohio State University) as part of University of Regin a topology seminar\n\n\nAbstract\nA long standing slogan in Goodwillie's f unctor calculus is that the derivatives of the identity functor on a suita ble model category should come equipped with a natural operad structure. A result of this type was first shown by Ching for the category of based to pological spaces. It has long been expected that in the category of algebr as over a reduced operad $\\mathcal{O}$ of spectra that the derivatives of the identity should be equivalent to $\\mathcal{O}$ as operads.\n\nIn thi s talk I will discuss my recent work which gives a positive answer to the above conjecture. My method is to induce a "highly homotopy coherent" oper ad structure on the derivatives of the identity via a pairing of underlyin g cosimplicial objects with respect to the box product. This cosimplicial object naturally arises by analyzing the derivatives of the Bousfield-Kan cosimplicial resolution of the identity via the stabilization adjunction f or $\\mathcal{O}$-algebras. Time permitting\, I will describe some additio nal applications of these box product pairings including a new description of an operad structure on the derivatives of the identity in spaces.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Niko Schonsheck (Ohio State University) DTSTART:20210128T223000Z DTEND:20210128T233000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/4 DESCRIPTION:Title: Fibration theorems\, functor calculus\, and chromatic connections i n $\\mathcal{O}$-algebras\nby Niko Schonsheck (Ohio State University) as part of University of Regina topology seminar\n\n\nAbstract\nBy conside ring algebras over an operad $\\mathcal{O}$ in one's preferred category of spectra\, we can encode various flavors of algebraic structure (e.g. comm utative ring spectra). Topological Quillen (TQ) homology is a naturally oc curring notion of homology for these objects\, with analogies to both sing ular homology and stabilization of spaces. In this talk\, we will begin by discussing a fibration theorem for TQ-completion\, showing that TQ-comple tion preserves fibration sequences in which the base and total $\\mathcal{ O}$-algebra are connected. We will then describe a few results that hint t owards an intrinsic connection between TQ-completion and the convergence o f the Taylor tower of the identity functor in the category of $\\mathcal{O }$-algebras. Lastly\, time permitting\, we will discuss recent joint work with Crichton Ogle on the chromatic localization of the homotopy completio n tower of $\\mathcal{O}$-algebras and connections to functor calculus.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Aziz Kharoof (Bilkent University) DTSTART:20210915T173000Z DTEND:20210915T183000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/5 DESCRIPTION:Title: Higher order Toda brackets\nby Aziz Kharoof (Bilkent University ) as part of University of Regina topology seminar\n\n\nAbstract\nToda bra ckets are a type of higher homotopy operation. Like Massey products\, they are not always defined\, and their value is indeterminate. Nevertheless\, they play an important role in algebraic topology and related fields. Tod a originally constructed them as a tool for computing homotopy groups of s pheres. Adams later showed that they can be used to calculate differential s in spectral sequences.\n\nAfter reviewing the construction and propertie s of the classical Toda bracket\, we shall describe a higher order version \, there are two ways to do that. We will provide a diagrammatic descripti on for the system we need to define the higher order Toda brackets\, then we will use that to give an alternative definition using the homotopy cofi ber.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Maximilien Péroux (University of Pennsylvania) DTSTART:20211102T210000Z DTEND:20211102T220000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/6 DESCRIPTION:Title: Equivariant variations of topological Hochschild homology\nby M aximilien Péroux (University of Pennsylvania) as part of University of Re gina topology seminar\n\n\nAbstract\nTopological Hochschild homology (THH) is an important variant for ring spectra. It is built as a geometric real ization of a cyclic bar construction. It is endowed with an action of circ le. This is because it is a geometric realization of a cyclic object. The simplex category factors through Connes’ category $\\Lambda$. Similarly\ , real topological Hochschild homology (THR) for ring spectra with anti-in volution is endowed with a $O(2)$-action. Here instead of the cyclic categ ory $\\Lambda$\, we use the dihedral category $\\Xi$.\n\nFrom work in prog ress with Gabe Angelini-Knoll and Mona Merling\, I present a generalizatio n of $\\Lambda$ and $\\Xi$ called crossed simplicial groups\, introduced b y Fiedorowicz and Loday. To each crossed simplical group $G$\, I define TH G\, an equivariant analogue of THH. Its input is a ring spectrum with a tw isted group action. THG is an algebraic invariant endowed with different a ction and cyclotomic structure\, and generalizes THH and THR.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Hana Jia Kong (Institute for Advanced Study) DTSTART:20220210T190000Z DTEND:20220210T200000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/7 DESCRIPTION:Title: Motivic image-of-J spectrum via the effective slice spectral sequen ce\nby Hana Jia Kong (Institute for Advanced Study) as part of Univers ity of Regina topology seminar\n\n\nAbstract\nThe "image-of-J" spectrum in the classical stable homotopy category has been well-studied\; Bachmann –Hopkins defined its motivic analogue. In this talk\, I will start with the classical story\, and then move to the motivic version. I will talk ab out the effective slice computation of the motivic "image-of-J" spectrum o ver the real numbers. Unlike the classical case\, the map from the motivic sphere is not surjective on homotopy groups. Still\, it captures a regula r pattern that appears in the $\\mathbb{R}$-motivic stable stems. This is joint work with Eva Belmont and Dan Isaksen.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/7/ END:VEVENT BEGIN:VEVENT SUMMARY:William Balderrama (University of Virginia) DTSTART:20220310T190000Z DTEND:20220310T200000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/8 DESCRIPTION:Title: The motivic lambda algebra and Hopf invariant one problem\nby W illiam Balderrama (University of Virginia) as part of University of Regina topology seminar\n\n\nAbstract\nCurrent best approaches to understanding the stable homotopy groups of spheres at the prime $2$ make use of the Ada ms spectral sequence\, which computes stable stems starting with informati on about the cohomology of the Steenrod algebra. The first major success o f the Adams spectral sequence was in Adams' resolution of the Hopf invaria nt one problem\, which proceeded via an analysis of secondary cohomology o perations. Later\, J.S.P. Wang used a certain algebraic device\, the lambd a algebra\, to give a more thorough computation of the cohomology of the S teenrod algebra\, and used this to give a slick almost entirely algebraic derivation of the Hopf invariant one theorem.\n\nIn this talk\, I will go over some of the above history\, and then describe work (joint with Domini c Culver and J.D. Quigley) on analogues in motivic stable homotopy theory. In particular\, I will describe a mod $2$ motivic lambda algebra\, define d over any base field of characteristic not equal to $2$\, as well as some of what can be said about the $1$-line of the motivic Adams spectral sequ ence for various base fields.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Sacha Ikonicoff (University of Calgary) DTSTART:20220414T190000Z DTEND:20220414T200000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/9 DESCRIPTION:Title: Divided power algebras over an operad\nby Sacha Ikonicoff (Univ ersity of Calgary) as part of University of Regina topology seminar\n\nLec ture held in RI 208 (Research and Innovation Centre).\n\nAbstract\nDivided power algebras were defined by H. Cartan in 1954 to study the homology of Eilenberg-MacLane spaces. They are commutative algebras endowed\, for eac h integer $n$\, with an additional monomial operation. Over a field of cha racteristic $0$\, this operation corresponds to taking each element to its $n$-th power divided by factorial of $n$. This definition does not make s ense if the base field is of prime characteristic\, yet Cartan's definitio n of divided power algebra applies in this situation as well. The notion o f divided power algebra over a field of prime characteristic allows us to describe algebraic structures that appear in homology and homotopical​ a lgebra and has found applications in a wide array of mathematical domains\ , for instance in crystalline cohomology\, and deformation theory.\n\nIn t his talk\, we will introduce the generalised definition of a divided power algebra over an operad given by B. Fresse in 2000. We will give a complet e characterisation for generalised divided power algebras in terms of mono mial operations and relations. We will show how to improve this characteri sation to particular cases\, including the case of a product of operads wi th distributive laws.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Martensen (NTNU Trondheim) DTSTART:20220919T190000Z DTEND:20220919T200000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/10 DESCRIPTION:Title: Triangulated categories and other $n$-angulations\nby Sebastia n Martensen (NTNU Trondheim) as part of University of Regina topology semi nar\n\n\nAbstract\nTriangulated categories were introduced to capture some of the extra structure present in the derived category of a ring and the stable homotopy category\, and today they are present wherever homological algebra plays a central role. In the case of derived categories\, the tri angulation captures certain “shadows” of short and long exact sequence s\, and so one may wonder: are there categories that capture only long exa ct sequences of a certain length? This led to the introduction of $n$-angu lated categories in 2013 by Geiss\, Keller\, and Oppermann. Today\, they f ind their use in representation theory\, and it is a hope that they will o ne day play a role in topology as well. For this talk we will discuss tria ngulated categories\, stable module categories\, and introduce $n$-angulat ed categories along with their main class of examples.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Petersen (MPIM Bonn) DTSTART:20221114T190000Z DTEND:20221114T200000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/11 DESCRIPTION:Title: The $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLa ne spaces\nby Sarah Petersen (MPIM Bonn) as part of University of Regi na topology seminar\n\n\nAbstract\nThis talk describes an extension of Rav enel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our main application and motivation for introducing these methods is a comput ation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacL ane spaces. The result we obtain for $C_2$-equivariant Eilenberg-MacLane s paces associated to the constant Mackey functor $\\underline{\\mathbb{F}}_ 2$ gives a $C_2$-equivariant analogue of the classical computation due to Serre at the prime $2$. We also investigate a twisted bar spectral sequenc e computing the homology of these equivariant Eilenberg-MacLane spaces.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Sikora (Bilkent University) DTSTART:20230131T190000Z DTEND:20230131T200000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/12 DESCRIPTION:Title: $RO(C_2)$-graded coefficients of $C_2$-Eilenberg-MacLane spectra\nby Igor Sikora (Bilkent University) as part of University of Regina to pology seminar\n\n\nAbstract\nIn non-equivariant topology\, the ordinary h omology of a point is described by the dimension axiom and is quite simple - namely\, it is concentrated in degree zero. The situation in $G$-equiva riant topology is different. This is because Bredon homology - the equivar iant counterpart of ordinary homology - is naturally graded over $RO(G)$\, the ring of $G$-representations. Whereas the equivariant dimension axiom describes the part of the Bredon homology of a point graded over trivial r epresentations\, it does not put any requirements on the rest of the gradi ng - in which the homology may be quite complicated.\n\nThe $RO(G)$-graded Bredon homology theories are represented by $G$-Eilenberg-MacLane spectra \, and thus the Bredon homology of a point is the same as coefficients of these spectra. During the talk\, I will present the method of computing th e $RO(C_2)$-graded coefficients of $C_2$-Eilenberg-MacLane spectra based o n the Tate square. As demonstrated by Greenlees\, the Tate square gives an algorithmic approach to computing the coefficients of equivariant spectra . In the talk\, we will discuss how to use this method to obtain the $RO(C _2)$-graded coefficients of a $C_2$-Eilenberg-MacLane spectrum as a $RO(C_ 2)$-graded abelian group. We will also present the multiplicative structur e of the $C_2$-Eilenberg-MacLane spectrum associated to the Burnside Macke y functor. Time permitting\, we will further discuss how to use this knowl edge to derive a multiplicative structure for the coefficients for any rin g Mackey functor.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Brandon Doherty (Stockholm University) DTSTART:20230411T190000Z DTEND:20230411T200000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/13 DESCRIPTION:Title: Cubical models of higher categories without connections\nby Br andon Doherty (Stockholm University) as part of University of Regina topol ogy seminar\n\n\nAbstract\nCubical sets with connections model $(\\infty\, 1)$-categories via the cubical Joyal model structure\, constructed and sho wn to be equivalent to the Joyal model structure on simplicial sets by Doh erty-Kapulkin-Lindsey-Sattler. In the same work\, an analogous model struc ture was constructed on the category of cubical sets without connections ( i.e.\, having only faces and degeneracies)\, but was not shown to be equiv alent to any other model of $(\\infty\,1)$-categories.\n\nIn this talk\, w e will review the cubical Joyal model structure on cubical sets without co nnections and discuss the proof that it is Quillen equivalent to the Joyal model structure on simplicial sets\, using a construction by which a fibr ant cubical set without connections can be equipped with connections via l ifting. This talk is based on the paper of the same title.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Sacha Ikonicoff (University of Ottawa) DTSTART:20230822T213000Z DTEND:20230822T223000Z DTSTAMP:20260422T225921Z UID:ReginaTopology/14 DESCRIPTION:Title: Quillen-Barr-Beck cohomology of divided power algebras over an ope rad\nby Sacha Ikonicoff (University of Ottawa) as part of University o f Regina topology seminar\n\nLecture held in RIC 208.\n\nAbstract\nDivided power algebras are algebras equipped with additional monomial operations. They are fairly ubiquitous in the positive characteristic setting\, and a ppear notably in the study of simplicial algebras\, in crystalline cohomol ogy\, and in deformation theory. An operad is a device that encodes operat ions: there is an operad for associative algebras\, one for commutative al gebras\, for Lie algebras\, Poisson algebras\, and so on. Each operad then comes with an associated category of algebras\, and also with a category of divided power algebras.\n\nThe aim of this talk is to show how André-Q uillen cohomology generalises to several categories of algebras using the notion of operad. We will introduce modules and derivations\, but also rep resenting objects for modules - known as the universal enveloping algebra - and for derivations - known as the module of Kähler differentials - whi ch will allow us to build an analogue of the cotangent complex. We will se e how these notions allow us to recover known cohomology theories on many categories of algebras\, while they provide somewhat exotic new notions wh en applied to divided power algebras.\n\nThis is joint work with Martin Fr ankland and Ioannis Dokas.\n LOCATION:https://researchseminars.org/talk/ReginaTopology/14/ END:VEVENT END:VCALENDAR