BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ran Levi (University of Aberdeen) DTSTART:20200420T140000Z DTEND:20200420T150000Z DTSTAMP:20260422T225754Z UID:OATS/1 DESCRIPTION:Title: Com plexes of Tournaments in Directed Networks\nby Ran Levi (University of Aberdeen) as part of Online algebraic topology seminar\n\n\nAbstract\nCli que graphs whose edges are oriented are referred to in the combinatorics l iterature as tournaments. We consider a family of semi-simplicial sets\, t hat we refer to as “tournaplexes"\, whose simplices are tournaments. In particular\, given a directed graph G\, we associate with it a “flag tou rnaplex" which is a tournaplex containing the directed flag complex of G\, but also the geometric realisation of cliques that are not directed. We d efine several types of filtration on tournaplexes\, and exploiting persist ent homology\, we observe that filtered flag tournaplexes provide finer me ans of distinguishing graph dynamics than the directed flag complex. We th en demonstrate the power of those ideas by applying them to graph data ari sing from the Blue Brain Project’s digital reconstruction of a rat’s n eocortex.\n LOCATION:https://researchseminars.org/talk/OATS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Andy Baker (University of Glasgow) DTSTART:20200427T140000Z DTEND:20200427T150000Z DTSTAMP:20260422T225754Z UID:OATS/2 DESCRIPTION:Title: Fun and games with the Steenrod algebra\nby Andy Baker (University of Gla sgow) as part of Online algebraic topology seminar\n\n\nAbstract\nThe mod 2 Steenrod algebra is an important tool in unstable and stable homotopy th eory but it is also interesting as a purely algebraic gadget. I will brief ly review its algebraic structure and that of some important finite subHo pf algebras. Then I will discuss some realisability questions for modules\ , ranging from classical examples to modules over the E-infinity ring spec tra kO and tmf localised at 2. I hope this talk will be accessible to begi nners and also have some things to interest experts.\n LOCATION:https://researchseminars.org/talk/OATS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Constanze Roitzheim (University of Kent) DTSTART:20200504T140000Z DTEND:20200504T150000Z DTSTAMP:20260422T225754Z UID:OATS/3 DESCRIPTION:Title: Equ ivariant homotopy commutativity\, trees and chicken feet\nby Constanze Roitzheim (University of Kent) as part of Online algebraic topology semin ar\n\n\nAbstract\nCommutativity up to homotopy can be daunting\, and it be comes even more difficult to track when equivariant structures get introdu ced. In the case of a finite group\, however\, the options for equivariant homotopy commutativity can be encoded using simple combinatorics\, and we will show some examples.\n LOCATION:https://researchseminars.org/talk/OATS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuele Dotto (University of Warwick) DTSTART:20200518T140000Z DTEND:20200518T150000Z DTSTAMP:20260422T225754Z UID:OATS/4 DESCRIPTION:Title: Wit t vectors with coefficients and characteristic polynomials over non-commut ative rings\nby Emanuele Dotto (University of Warwick) as part of Onli ne algebraic topology seminar\n\n\nAbstract\nThe characteristic polynomial of a matrix with entries in a commutative ring $R$ naturally takes value in the ring of Witt vectors of $R$. In joint work with Krause\, Nikolaus a nd Patchkoria\, we extend the classical Witt vectors construction to allow as input pairs of a ring $R$ and a bimodule $M$. I will explain how this construction relates to topological Hochschild homology\, the Hill-Hopkins -Ravenel norm\, and the characteristic polynomial.\n LOCATION:https://researchseminars.org/talk/OATS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathryn Hess (EPFL) DTSTART:20200608T140000Z DTEND:20200608T150000Z DTSTAMP:20260422T225754Z UID:OATS/5 DESCRIPTION:Title: Cal culus from comonads\nby Kathryn Hess (EPFL) as part of Online algebrai c topology seminar\n\n\nAbstract\n(Joint work with Brenda Johnson.) The m any theories of "calculus" introduced in algebraic topology over the past couple of decades--e.g.\, Goodwillie's calculus of homotopy functors\, the Goodwillie-Weiss manifold calculus\, the orthogonal calculus\, and the Jo hnson-McCarthy cotriple calculus--all have a similar flavor\, though the o bjects studied and exact methods applied are not the same. We have const ructed a relatively simple category-theoretic machine for producing towers of functors from a small category into a simplicial model category\, dete rmined conditions under which such tower-building machines constitute a ca lculus\, and showed that this framework encompasses certain well known cal culi\, as well as providing new classes of examples. The cogs and gears of our machine are cubical diagrams of reflective subcategories and the co monads they naturally give rise to.\n\nIn this talk\, I will assume no fam iliarity with comonads and only basic knowledge of simplicial model catego ries.\n LOCATION:https://researchseminars.org/talk/OATS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Adams (Colorado State University) DTSTART:20200525T140000Z DTEND:20200525T150000Z DTSTAMP:20260422T225754Z UID:OATS/6 DESCRIPTION:Title: Vie toris-Rips complexes and Borsuk-Ulam theorems\nby Henry Adams (Colorad o State University) as part of Online algebraic topology seminar\n\n\nAbst ract\nGiven a metric space X and a scale parameter r\, the Vietoris-Rips s implicial complex VR(X\;r) has X as its vertex set\, and contains a finite subset as a simplex if its diameter is at most r. Vietoris-Rips complexes were invented by Vietoris in order to define a (co)homology theory for me tric spaces\, and by Rips for use in geometric group theory. More recently \, they have found applications in computational topology for approximatin g of the shape of a dataset. I will explain how the Vietoris-Rips complexe s of the circle\, as the scale parameter r increases\, obtain the homotopy types of the circle\, the 3-sphere\, the 5-sphere\, the 7-sphere\, ...\, until they are finally contractible. Only very little is understood about the homotopy types of the Vietoris-Rips complexes of the n-sphere. Knowing the homotopy connectivities of Vietoris-Rips complexes of spheres allows one to prove generalizations of the Borsuk-Ulam theorem for maps from the n-sphere into k-dimensional Euclidean space with k > n. Joint work with Jo hn Bush and Florian Frick.\n LOCATION:https://researchseminars.org/talk/OATS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Kirsten Wickelgren (Duke University) DTSTART:20200601T140000Z DTEND:20200601T150000Z DTSTAMP:20260422T225754Z UID:OATS/7 DESCRIPTION:Title: The re are 160\,839<1> + 160\,650<-1> 3-planes in a 7-dimensional cubic hypers urface\nby Kirsten Wickelgren (Duke University) as part of Online alge braic topology seminar\n\n\nAbstract\nThe expression in the title is a bil inear form and it comes from an Euler number in A1-algebraic topology. Suc h Euler numbers can be constructed with Hochschild homology\, self-duality of Koszul complexes\, pushforwards in SL_c oriented cohomology theories\, and sums of local degrees. We show an integrality result for A1-Euler num bers and apply this to the enumeration of d-planes in complete intersectio ns. Classically such counts are valid over C and sometimes extended to the real numbers\, but A1-homotopy theory allows one to perform counts over a large class of fields\, and records information about the solutions in bi linear form. The example in the title then follows from work of Finashin-- Kharlamov. This is joint work with Tom Bachmann.\n LOCATION:https://researchseminars.org/talk/OATS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Szymik (NTNU) DTSTART:20200615T140000Z DTEND:20200615T150000Z DTSTAMP:20260422T225754Z UID:OATS/8 DESCRIPTION:Title: Tri graded spectral sequences for principal fibrations\nby Markus Szymik ( NTNU) as part of Online algebraic topology seminar\n\n\nAbstract\nThe Lera y--Serre and the Eilenberg--Moore spectral sequence are fundamental tools for computing the cohomology of a group or\, more generally\, of a space. In joint work with Frank Neumann (Leicester)\, we describe the relationsh ip between these two spectral sequences in the situation when both of them share the same abutment. This talk is an introduction to the topic with many examples. It should be suitable for an audience from graduate studen ts in algebraic topology onward\, and I will only assume some casual acqua intance with spectral sequences.\n LOCATION:https://researchseminars.org/talk/OATS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Ulrich Pennig (Cardiff University) DTSTART:20200511T140000Z DTEND:20200511T150000Z DTSTAMP:20260422T225754Z UID:OATS/9 DESCRIPTION:Title: Loo ps\, groups\, and twists - the role of K-theory in mathematical physics\nby Ulrich Pennig (Cardiff University) as part of Online algebraic topol ogy seminar\n\n\nAbstract\nWhile K-theory has its origins in Grothendieck' s formulation and proof of his version of the Riemann-Roch theorem\, it no w plays a significant role in many diverse branches of mathematics: It pro vides a fundamental example of a cohomology theory\, and it is one of the most important invariants of C*-algebras. In the first half of the talk\, I will define the K-groups and discuss some of their applications. In the second half\, I will concentrate on equivariant twisted K-theory\, which i s related to the representation theory of loop groups and the geometry of two-dimensional quantum field theories by a theorem of Freed\, Hopkins\, a nd Teleman. I will finish with an outline of joint work with D. Evans\, in which we study generalizations of this work to higher twists.\n LOCATION:https://researchseminars.org/talk/OATS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Hahn (MIT) DTSTART:20200921T130000Z DTEND:20200921T140000Z DTSTAMP:20260422T225754Z UID:OATS/10 DESCRIPTION:Title: Ni shida Nilpotence\nby Jeremy Hahn (MIT) as part of Online algebraic top ology seminar\n\n\nAbstract\nIn 1973\, Nishida proved that every positive degree class in the stable homotopy groups of spheres is nilpotent. We wi ll discuss some modern perspectives on Nishida's original proof. While th is will be a mostly expository talk aimed at graduate students\, if time p ermits we will end with a discussion of some open nilpotence questions in motivic stable homotopy theory.\n LOCATION:https://researchseminars.org/talk/OATS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Lennart Meier (Utrecht) DTSTART:20200928T140000Z DTEND:20200928T150000Z DTSTAMP:20260422T225754Z UID:OATS/11 DESCRIPTION:Title: El liptic cohomology of level n\nby Lennart Meier (Utrecht) as part of On line algebraic topology seminar\n\n\nAbstract\nElliptic genera have played an important role in algebraic topology and algebraic geometry since the 1980s. To every almost-complex manifold they associate a modular form for the congruence subgroups $\\Gamma_1(n)$. More recently\, elliptic cohomolo gy theories have been built that are natural targets of elliptic genera fo r families. I will give an overview of these theories and report in partic ular on certain $C_2$-equivariant refinements.\n LOCATION:https://researchseminars.org/talk/OATS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Viktoriya Ozornova (Ruhr-Universität Bochum) DTSTART:20201005T140000Z DTEND:20201005T150000Z DTSTAMP:20260422T225754Z UID:OATS/12 DESCRIPTION:Title: Mo dels of (infty\,2)-categories\nby Viktoriya Ozornova (Ruhr-Universitä t Bochum) as part of Online algebraic topology seminar\n\n\nAbstract\nAn $ (\\infty\,2)$-category should be a weak version of a strict $2$-category\, in which compositions are well-defined\, associative and unital up to som e higher coherence. There are various models making this precise. In this talk\, I will describe a direct comparison between two particular models ( which will be introduced)\, namely $\\Theta_2$-spaces and saturated $2$-co mplicial sets. This is joint work in progress with Julie Bergner and Marti na Rovelli.\n LOCATION:https://researchseminars.org/talk/OATS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Birgit Richter (Universität Hamburg) DTSTART:20201019T140000Z DTEND:20201019T150000Z DTSTAMP:20260422T225754Z UID:OATS/13 DESCRIPTION:Title: De tecting and describing ramification for structured ring spectra\nby Bi rgit Richter (Universität Hamburg) as part of Online algebraic topology s eminar\n\n\nAbstract\nThis is a report on joint work in progress with Eva Höning. \n\nRamification for commutative ring spectra can be detected by relative topological Hochschild homology and by the spectrum of Kähler di fferentials. For rings of integers in an extension of number fields\, it i s important to distinguish between tame and wild ramification. Noether's t heorem characterizes tame ramification in terms of a normal basis and tame ramification can also be detected via the surjectivity of the norm map. W e take the latter fact and use the Tate cohomology spectrum to detect wild ramification in the context of commutative ring spectra. In the talk\, I will discuss several examples in the context of topological K-theory and m odular forms.\n LOCATION:https://researchseminars.org/talk/OATS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Drew Heard (NTNU) DTSTART:20201102T150000Z DTEND:20201102T160000Z DTSTAMP:20260422T225754Z UID:OATS/14 DESCRIPTION:Title: Su pport theory for triangulated categories in algebra and topology\nby D rew Heard (NTNU) as part of Online algebraic topology seminar\n\n\nAbstrac t\nWe will survey the support theory of triangulated categories through th e machinery of tensor-triangulated geometry. We will discuss the stratific ation theory of Benson—Iyengar—Krause for triangulated categories\, th e construction by Balmer of the spectrum of a tensor-triangulated category \, and the relation between the two. Time permitting\, we will discuss a r ecent application to the category of derived Mackey functors\, joint with Beren Sanders.\n LOCATION:https://researchseminars.org/talk/OATS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Julie Bergner (University of Virginia) DTSTART:20201130T150000Z DTEND:20201130T160000Z DTSTAMP:20260422T225754Z UID:OATS/15 DESCRIPTION:Title: Va riants of the Waldhausen S-construction\nby Julie Bergner (University of Virginia) as part of Online algebraic topology seminar\n\n\nAbstract\nT he S-construction\, first defined in the setting of cofibration categories by Waldhausen\, gives a way to define the algebraic K-theory associated t o certain kinds of categorical input. It was proved by Galvez-Carrillo\, Kock\, and Tonks that the result of applying this construction to an exact category is a decomposition space\, also called a 2-Segal space\, and Dyc kerhoff and Kapranov independently proved the same result for the slightly more general input of proto-exact categories. In joint work with Osorno\ , Ozornova\, Rovelli\, and Scheimbauer\, we proved that these results can be maximally generalized to the input of augmented stable double Segal spa ces\, so that the S-construction defines an equivalence of homotopy theori es. In this talk\, we'll review the S-construction and the reasoning behi nd these stages of generalization. Time permitting\, we'll discuss attemp ts to characterize those augmented stable double Segal spaces that corresp ond to cyclic spaces\, which is work in progress with Walker Stern.\n LOCATION:https://researchseminars.org/talk/OATS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Marie Bohmann (Vanderbilt) DTSTART:20201110T150000Z DTEND:20201110T160000Z DTSTAMP:20260422T225754Z UID:OATS/16 DESCRIPTION:Title: Al gebraic K-theory for Lawvere theories: assembly and Morita invariance\ nby Anna Marie Bohmann (Vanderbilt) as part of Online algebraic topology seminar\n\n\nAbstract\nMuch like operads and monads\, Lawvere theories are a way of encoding algebraic structures\, such as those of modules over a ring or sets with a group action. In this talk\, we discuss the algebraic K-theory of Lawvere theories\, which contains information about automorph ism groups of these structures. We'll discuss both particular examples an d general constructions in the K-theory of Lawvere theories\, including ex amples showing the limits of Morita invariance and the construction of ass embly-style maps. This is joint work with Markus Szymik.\n LOCATION:https://researchseminars.org/talk/OATS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Angélica Osorno (Reed) DTSTART:20201012T150000Z DTEND:20201012T160000Z DTSTAMP:20260422T225754Z UID:OATS/17 DESCRIPTION:Title: Tr ansfer systems and weak factorization systems\nby Angélica Osorno (Re ed) as part of Online algebraic topology seminar\n\n\nAbstract\n$N_\\infty $ operads over a group G encode homotopy commutative operations together w ith a class of equivariant transfer (or norm) maps. Their homotopy theory is given by transfer systems\, which are certain discrete objects that hav e a rich combinatorial structure defined in terms of the subgroup lattice of G. In this talk\, we will show that when G is finite Abelian\, transfer systems are in bijection with weak factorization systems on the poset cat egory of subgroups of G. This leads to an involution on the lattice of tra nsfer systems\, generalizing the work of Balchin–Bearup–Pech–Roitzhe im for cyclic groups of squarefree order. We will conclude with an enumera tion of saturated transfer systems and comments on the Rubin and Blumberg –Hill saturation conjecture.\n\nThis is joint work with Evan Franchere\, Usman Hafeez\, Peter Marcus\, Kyle Ormsby\, Weihang Qin\, and Riley Waugh .\n LOCATION:https://researchseminars.org/talk/OATS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Rivera (Purdue) DTSTART:20201123T150000Z DTEND:20201123T160000Z DTSTAMP:20260422T225754Z UID:OATS/18 DESCRIPTION:Title: Th e coalgebra of chains and the fundamental group\nby Manuel Rivera (Pur due) as part of Online algebraic topology seminar\n\n\nAbstract\nRational homotopy theory tells us that simply connected spaces\, up to rational hom otopy equivalence\, may be classified algebraically by means of rational c ocommutative coalgebras (Quillen) or in the finite type case by rational d g commutative algebras (Sullivan). Goerss and Mandell proved versions of t hese results for fields of arbitrary characteristic by means of simplicial cocommutative coalgebras and E-infinity algebras\, respectively. The alge braic structures in these settings are considered up to quasi-isomorphism. \nIn this talk\, I will describe how to extend these results to spaces wit h arbitrary fundamental group.The key new observation is that the homotopy cocommutative coalgebraic structure of the chains on a space determines t he fundamental group in complete generality. The corresponding algebraic n otion of weak equivalence between coalgebras is drawn from Koszul duality. The end goal of this program is to completely understand homotopy types i n terms of algebraic “chain level” structure. This is joint work with M. Zeinalian and F. Wierstra.\n LOCATION:https://researchseminars.org/talk/OATS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Whitehouse (Sheffield) DTSTART:20201116T150000Z DTEND:20201116T160000Z DTSTAMP:20260422T225754Z UID:OATS/19 DESCRIPTION:Title: Mo del category structures and spectral sequences\nby Sarah Whitehouse (S heffield) as part of Online algebraic topology seminar\n\n\nAbstract\nI'll discuss a family of model category structures such that weak equivalences are morphisms inducing an isomorphism at a fixed stage of a spectral sequ ence. The talk will focus on joint work with Xin Fu\, Ai Guan and Muriel L ivernet\, giving such model structures for multicomplexes. A multicomplex (also known as a twisted chain complex) is an algebraic structure generali zing the notion of a chain complex and that of a bicomplex. These structur es have arisen in many different places and play an important role in homo logical and homotopical algebra.\n LOCATION:https://researchseminars.org/talk/OATS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Grigory Garkusha (Swansea) DTSTART:20201026T160000Z DTEND:20201026T170000Z DTSTAMP:20260422T225754Z UID:OATS/20 DESCRIPTION:Title: Mo tivic Gamma-spaces\nby Grigory Garkusha (Swansea) as part of Online al gebraic topology seminar\n\n\nAbstract\nThis is a joint work with Ivan Pan in and Paul Arne Østvær. We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectr a in the algebro-geometric setting of motivic homotopy theory. Our approac h combines Gamma-spaces and framed correspondences into the concept of mot ivic Gamma-spaces\; these are continuous or enriched functors of two varia bles that take values in motivic spaces and are equipped with a framing. W e craft proofs of our main results by imposing further axioms on motivic G amma-spaces such as a Segal condition for simplicial Nisnevich sheaves\, c ancellation\, A1- and sigma-invariance\, Nisnevich excision\, Suslin contr actibility\, and grouplikeness. This adds to the discussion in the literat ure on coexisting points of view on the A1-homotopy theory of algebraic va rieties. As prime examples we discuss the motivic sphere spectrum\, algebr aic cobordism\, motivic cohomology\, and Milnor-Witt motivic cohomology.\n LOCATION:https://researchseminars.org/talk/OATS/20/ END:VEVENT END:VCALENDAR