BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hood Chatham (MIT) DTSTART:20200406T203000Z DTEND:20200406T213000Z DTSTAMP:20260422T212708Z UID:MITTop/1 DESCRIPTION:Title: A n orientation map for height $p−1$ real $E$ theory\nby Hood Chatham (MIT) as part of MIT topology seminar\n\n\nAbstract\nLet $p$ be an odd pri me and let $\\operatorname{EO}=E^{hC_p}_{p−1}$ be the $C_p$ fixed points of height $p−1$ Morava $E$ theory. We say that a spectrum $X$ has algeb raic $\\operatorname{EO}$ theory if the splitting of $K_*(X)$ as an $K_*[C _p]$ module lifts to a topological splitting of $\\operatorname{EO} \\wedg e X$. We develop criteria to show that a spectrum has algebraic $\\operato rname{EO}$ theory\, in particular showing that any connnective spectrum wi th mod $p$ homology concentrated in degrees $2k(p−1)$ has algebraic $\\o peratorname{EO}$ theory. As an application\, we answer a question posed by Hovey and Ravenel by producing a unital orientation $MW_{4p−4} \\to \\o peratorname{EO}$ analogous to the $MSU$ orientation of $KO$ at $p=2$ where $MW_{4p−4}$ is the Thom spectrum of the $(4p−4)$-connective Wilson sp ace.\n LOCATION:https://researchseminars.org/talk/MITTop/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Campbell (Duke) DTSTART:20200413T203000Z DTEND:20200413T213000Z DTSTAMP:20260422T212708Z UID:MITTop/2 DESCRIPTION:Title: H omotopy theory and Hilbert’s third problem\nby Jonathan Campbell (Du ke) as part of MIT topology seminar\n\n\nAbstract\nIn this talk I'll expla in how one might attack Hilbert's Generalized Third Problem via homotopy t heory\, and describe recent progress in this direction. Two $n$-dimensiona l polytopes\, $P$\, $Q$ are said to be scissors congruent if one can cut $ P$ along a finite number of hyperplanes\, and re-assemble the pieces into $Q$. The scissors congruence problem\, aka Hilbert's Generalized Third Pro blem\, asks: when can we do this? what obstructs this? In two dimensions\, two polygons are scissors congruent if and only if they have the same are a. In three dimensions\, there is volume and another invariant\, the Dehn Invariant. In higher dimensions\, very little is known — but the problem is known to have deep connections to motives\, values of zeta functions\, the weight filtration in algebraic K-theory\, and regulator maps. I'll gi ve a leisurely introduction to this very classical problem\, and explain s ome new results obtained via homotopy theoretic techniques. This is joint work with Inna Zakharevich.\n LOCATION:https://researchseminars.org/talk/MITTop/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Ching (Amherst College) DTSTART:20200427T203000Z DTEND:20200427T213000Z DTSTAMP:20260422T212708Z UID:MITTop/3 DESCRIPTION:Title: T angent ∞-categories and Goodwillie calculus\nby Michael Ching (Amher st College) as part of MIT topology seminar\n\n\nAbstract\n(Joint with Kri stine Bauer and Matthew Burke.) Lurie defines the “tangent bundle” to an ∞-category C to be the ∞-category of excisive functors from finite pointed spaces to C. In this talk\, I will describe an abstract framework which includes both this construction and the ordinary tangent bundle func tor on the category of smooth manifolds (as well as many other examples). That framework is an extension to ∞-categories of the “tangent categor ies” of Cockett and Cruttwell (based on earlier work of Rosický).\n\nTh ose authors and others have explored the extent to which various concepts from differential geometry\, such as connections\, curvature and cohomolog y\, can be developed abstractly within a tangent category. Thus our result provides a framework for “doing” differential geometry in the context of Goodwillie’s calculus of functors. For example\, we show that Goodwi llie’s notion of n-excisive functor can be recovered from the general no tion of “n-jet” in a tangent category.\n LOCATION:https://researchseminars.org/talk/MITTop/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhouli Xu (MIT) DTSTART:20200504T203000Z DTEND:20200504T213000Z DTSTAMP:20260422T212708Z UID:MITTop/4 DESCRIPTION:Title: S table stems and the Chow-Novikov t-structure in motivic stable homotopy ca tegory\nby Zhouli Xu (MIT) as part of MIT topology seminar\n\n\nAbstra ct\nIn this talk\, I will discuss recent progress on the computation of cl assical stable homotopy groups of spheres\, and highlight some new results regarding certain Adams differentials and their connections to the Kervai re invariant classes. These computations use the Chow-Novikov t-structure on the cellular motivic stable homotopy theory over C in an essential way. I will also discuss a recent result that extends this t- structure to the non-cellular part of the category which holds over any field\, and its po tential applications in computations.\n\nThis talk is based on several joi nt projects involving Tom Bachmann\, Robert Burklund\, Bogdan Gheorghe\, D an Isak- sen\, Hana Jia Kong and Guozhen Wang.\n\nFor information\, write: burklund@mit.edu\n LOCATION:https://researchseminars.org/talk/MITTop/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Tyler Lawson (University of Minnesota) DTSTART:20200511T203000Z DTEND:20200511T213000Z DTSTAMP:20260422T212708Z UID:MITTop/5 DESCRIPTION:Title: O bstruction theory for ring spectra\nby Tyler Lawson (University of Min nesota) as part of MIT topology seminar\n\n\nAbstract\nI'll discuss calcul ational methods for determining moduli of objects and maps between $E_\\in fty$ ring spectra\, and the relation to topological Andre-Quillen cohomolo gy.\n LOCATION:https://researchseminars.org/talk/MITTop/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Yakerson (Regensburg University) DTSTART:20200721T160000Z DTEND:20200721T170000Z DTSTAMP:20260422T212708Z UID:MITTop/6 DESCRIPTION:Title: N ew Models for Motivic K-Theory Spectra\nby Maria Yakerson (Regensburg University) as part of MIT topology seminar\n\n\nAbstract\nAlgebraic and h ermitian K-theories of smooth schemes are generalized cohomology theories\ , represented in the motivic stable homotopy category. In this talk\, we explain how to obtain new geometric models for the corresponding motivic s pectra\, based on the specific kinds of transfer maps that these cohomolog y theories acquire.  As a surprising side-effect\, we compute the motivic homotopy type of the Hilbert scheme of infinite affine space.  This is j oint work with Marc Hoyois\, Jochim Jelisiejew\, Denis Nardin and Burt Tot aro.\n\nFor information\, write: adelayyz@mit.edu\n LOCATION:https://researchseminars.org/talk/MITTop/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Dustin Clausen (Max Plank Institute) DTSTART:20200728T160000Z DTEND:20200728T170000Z DTSTAMP:20260422T212708Z UID:MITTop/7 DESCRIPTION:Title: T he Linearization Hypothesis\nby Dustin Clausen (Max Plank Institute) a s part of MIT topology seminar\n\n\nAbstract\nLazard showed that the conti nuous group cohomology of a large class ofp-adic Lie groups\, with p-adic coefficients\, satisfies Poincare duality. Analogously to the usual Poinca re duality of real manifolds\, there are orientability issues\, but Lazard showed that the relevant orientation local system is completely determine d by the adjoint representation of the group in an explicit manner\, allow ing for an easy analysis. This can be compared to how the orientation loc al system on a real manifold is determined by the tangent bundle\, a very useful "linearization" of the problem. Now\, there is an analogous Poinca re duality with spectrum coefficients both in the setting of p-adic Lie gr oups and in the setting of real manifolds. In the latter case the relevan t orientation local system is still determined by the tangent bundle\; in fact it is the suspension spectrum of the associated sphere bundle\, a sta tement known as Atiyah duality. In the former case\, there is a natural g uess for how the orientation local system should still be determined by th e adjoint representation. This has been highlighted by recent work of Bea udry-Goerss-Hopkins-Stojanoska in their study of duality for tmf\, and the y dubbed this guess the "linearization hypothesis". Neither Lazard's tech niques nor the usual arguments for Atiyah duality can be used to attack th e\nlinearization hypothesis. In this talk I will explain a proof of the l inearization hypothesis\, whose main ingredients are a deformation of any p-adic Lie group to its Lie algebra\, and a rather exotic "cospecializatio n map" which lets you use this deformation to jump from the Lie algebra to the Lie group as if the deformation were parametrized by a unit interval\ , even though it is only parametrized by a totally disconnected space.\n LOCATION:https://researchseminars.org/talk/MITTop/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Antieau (University of Illinois at Chicago and Northweste rn University) DTSTART:20200804T160000Z DTEND:20200804T170000Z DTSTAMP:20260422T212708Z UID:MITTop/8 DESCRIPTION:Title: H igher Brauer groups\nby Benjamin Antieau (University of Illinois at Ch icago and Northwestern University) as part of MIT topology seminar\n\n\nAb stract\nI will give an introduction to the idea of higher Brauer groups\, focusing on the "next" higher Brauer group\, consisting of Morita equivale nce classes of certain Azumaya categories. The emphasis of the talk will b e on analogies\, examples\, calculations\, and open problems.\n LOCATION:https://researchseminars.org/talk/MITTop/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Nikolaus (Münster) DTSTART:20200811T160000Z DTEND:20200811T170000Z DTSTAMP:20260422T212708Z UID:MITTop/9 DESCRIPTION:Title: O n Grothendieck--Witt theory of the integers.\nby Thomas Nikolaus (Mün ster) as part of MIT topology seminar\n\n\nAbstract\nWe introduce the Grot hendieck--Witt groups of the integers and the Grothendieck--Witt spectrum of the integers. Then we explain how to compute these groups and the homot opy type of the spectrum using recent work on K-theory and L-theory. If ti me permits we also explain how to resolve the homotopy limit problem for r ings of integers in number fields and prove Karoubi's periodicity conjecur e for arbitrart rings.\n LOCATION:https://researchseminars.org/talk/MITTop/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Marc Hoyois (Regensburg University) DTSTART:20200818T160000Z DTEND:20200818T170000Z DTSTAMP:20260422T212708Z UID:MITTop/10 DESCRIPTION:Title: Milnor excision for motivic spectra\nby Marc Hoyois (Regensburg Univer sity) as part of MIT topology seminar\n\n\nAbstract\nIt is a classical res ult of Weibel that homotopy invariant algebraic\nK-theory satisfies excisi on\, in the sense that for any ring A and ideal I ⊂ A\,\nthe fiber of K H(A) → KH(A/I) depends only on I as a nonunital ring. In joint\nwork wit h Elden Elmanto\, Ryomei Iwasa\, and Shane Kelly\, we show that this is\nt rue more generally for any cohomology theory represented by a motivic spec trum.\n LOCATION:https://researchseminars.org/talk/MITTop/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Rune Haugseng (Norwegian University of Science and Technology) DTSTART:20200825T160000Z DTEND:20200825T170000Z DTSTAMP:20260422T212708Z UID:MITTop/11 DESCRIPTION:by Rune Haugseng (Norwegian University of Science and Technolo gy) as part of MIT topology seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MITTop/11/ END:VEVENT BEGIN:VEVENT SUMMARY:David Gepner (University of Illinois at Chicago) DTSTART:20200921T203000Z DTEND:20200921T213000Z DTSTAMP:20260422T212708Z UID:MITTop/12 DESCRIPTION:Title: Elliptic cohomology of the unitary group\nby David Gepner (University of Illinois at Chicago) as part of MIT topology seminar\n\n\nAbstract\nWe aim to show that the elliptic cohomology of the (classifying stack\nof the ) unitary group can be calculated as the ring of functions on the Hilbert\ nscheme of points of the associated derived elliptic curve. To this end\, we will\nbegin with a discussion of (integral) equivariant elliptic cohomo logy\, due to\nJacob Lurie\, using the formalism of orbispaces\, as develo ped by myself and Andre\nHenriques. This is joint work with Lennart Meier. \n LOCATION:https://researchseminars.org/talk/MITTop/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Adeel Khan (Regensburg University) DTSTART:20200928T203000Z DTEND:20200928T213000Z DTSTAMP:20260422T212708Z UID:MITTop/13 DESCRIPTION:Title: Derived cycle classes\nby Adeel Khan (Regensburg University) as part o f MIT topology seminar\n\n\nAbstract\nLet X be a smooth complex algebraic variety. In contrast with the situation for the singular homology groups H _*(X)\, the construction of intersection products on the Chow groups of X is subtle due to the comparative difficulty in dealing with non-transverse intersections. I will explain one way to deal with this problem by consid ering cycle classes that come from derived algebraic geometry. In combinat ion with the algebraic analogue of Steenrod's problem on resolution of sin gularities of homology classes (which holds by Hironaka)\, this yields a n ew construction of cup products in Chow groups. Time permitting\, I may al so discuss how derived cycle classes arise in motivic homotopy theory.\n LOCATION:https://researchseminars.org/talk/MITTop/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Campbell (Center for Communications Research La Jolla) DTSTART:20201005T203000Z DTEND:20201005T213000Z DTSTAMP:20260422T212708Z UID:MITTop/14 DESCRIPTION:Title: Homotopy Theory and Hilbert's Third Problem\nby Jonathan Campbell (Cen ter for Communications Research La Jolla) as part of MIT topology seminar\ n\n\nAbstract\nIn this talk I'll explain how one might attack Hilbert's Ge neralized Third\nProblem via homotopy theory\, and describe recent progres s in this direction. Two\nn-dimensional polytopes\, $P$\, $Q$ are said to be scissors congruent if one can\ncut $P$ along a finite number of hyperpl anes\, and re-assemble the pieces into\n$Q$. The scissors congruence probl em\, aka Hilbert's Generalized Third Problem\,\nasks: when can we do this? What obstructs this? In two dimensions\, two polygons\nare scissors congr uent if and only if they have the same area. In three\ndimensions\, there is volume and another invariant\, the Dehn Invariant. In higher\ndimension s\, very little is known --- but the problem is known to have deep\nconnec tions to motives\, values of zeta functions\, the weight filtration in\nal gebraic K-theory\, and regulator maps. I'll give a leisurely introduction to\nthis very classical problem\, and explain some new results obtained vi a homotopy\ntheoretic techniques. This is all joint with Inna Zakharevich .\n\n\n\nAdd this seminar to your calendar : http://math.mit.edu/topology/ topology_seminar.ics\n LOCATION:https://researchseminars.org/talk/MITTop/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Knudsen (Northeastern University) DTSTART:20201019T203000Z DTEND:20201019T213000Z DTSTAMP:20260422T212708Z UID:MITTop/15 DESCRIPTION:Title: Smooth structures and embedding calculus\nby Ben Knudsen (Northeastern University) as part of MIT topology seminar\n\n\nAbstract\nWe ask when em bedding calculus can distinguish pairs of smooth\nmanifolds that are homeo morphic but not diffeomorphic. We prove that\, in\ndimension 4\, the answe r is “almost never.” In contrast\, we exhibit an infinite\nlist of hig h-dimensional exotic spheres detected by embedding calculus. The\nformer r esult implies that the algebraic topology of knot spaces is insensitive\nt o smooth structure in dimension 4\, answering a question of Viro. The latt er\nresult gives a partial answer to a question of Francis and hints at th e\npossibility of a new classification of exotic spheres in terms of a str atified\nobstruction theory applied to compactified configuration spaces. This talk\nrepresents joint work with Alexander Kupers.\n\n\n\nAdd this to your calendar : http://math.mit.edu/topology/topology_seminar.ics\n LOCATION:https://researchseminars.org/talk/MITTop/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcy Robertson (University of Melbourne) DTSTART:20201026T203000Z DTEND:20201026T213000Z DTSTAMP:20260422T212708Z UID:MITTop/16 DESCRIPTION:Title: Expansions\, completions and automorphisms of welded tangled foams\nby Marcy Robertson (University of Melbourne) as part of MIT topology seminar \n\n\nAbstract\nWelded tangles are knotted surfaces in $\\mathbb{R}^4$. Ba r-Natan and Dancso described a class of welded tangles which have “foame d vertices” where one allows surfaces to merge and split. The resulting welded tangled foams carry an algebraic structure\, similar to the planar algebras of Jones\, called a circuit algebra. In joint work with Dancso an d Halacheva we provide a one-to-one correspondence between circuit algebra s and a form of rigid tensor category called ``wheeled props.'' This is a higher dimensional version of the well-known algebraic classification of p lanar algebras as certain pivotal categories.\n\n\nThis classification all ows us to connect these ``welded tangled foams\,'' to the Kashiwara-Vergne conjecture in Lie theory. In work in progress\, we show that the group of homotopy automorphisms of the (rational completion of) the wheeled prop o f welded foams is isomorphic to the group of symmetries KV\, which acts on the solutions to the Kashiwara-Vergne conjecture. Moreover\, we explain\n how this approach illuminates the close relationship between the group KV and the pro-unipotent Grothendieck--Teichmüller group.\n LOCATION:https://researchseminars.org/talk/MITTop/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Hausmann (Universität Bonn) DTSTART:20200630T160000Z DTEND:20200630T170000Z DTSTAMP:20260422T212708Z UID:MITTop/17 DESCRIPTION:Title: Global group laws and the equivariant Quillen theorem\nby Markus Hausm ann (Universität Bonn) as part of MIT topology seminar\n\n\nAbstract\nI w ill discuss an equivariant version of Quillen's theorem that the complex b ordism ring carries the universal formal group law\, both over a fixed abe lian group and in a global equivariant setting.\n LOCATION:https://researchseminars.org/talk/MITTop/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Agnès Beaudry (University of Colorado Boulder) DTSTART:20201116T213000Z DTEND:20201116T223000Z DTSTAMP:20260422T212708Z UID:MITTop/18 DESCRIPTION:Title: Equivariant Morava K-Theories?\nby Agnès Beaudry (University of Color ado Boulder) as part of MIT topology seminar\n\n\nAbstract\nAt height $h=2 ^{n-1}m$\, the Morava stabilizer group contains a cyclic group $G$\nof ord er $2^n$. In this talk\, I will present equivariant spectra that refine th e\nclassical height $h$ Morava $K$-theories. These are obtained from\n$G$- equivariant models of Lubin-Tate spectra which were constructed in recent\ njoint work with Hill-Shi-Zeng. I will present some preliminary results a nd\nconjectures about their slice filtration and equivariant homotopy grou ps and\ndiscuss how exotic transchromatic extensions lead to interesting d ifferentials.\n\nThis is joint work with Hill-Shi-Zeng.\n LOCATION:https://researchseminars.org/talk/MITTop/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Pstragowski (Harvard) DTSTART:20201102T213000Z DTEND:20201102T223000Z DTSTAMP:20260422T212708Z UID:MITTop/19 DESCRIPTION:Title: Franke's algebraicity conjecture\nby Piotr Pstragowski (Harvard) as pa rt of MIT topology seminar\n\n\nAbstract\nIn 1996\, Jens Franke conjecture d that any stable infinity-category possessing an Adams spectral sequence whose sparsity is greater than the homological dimension\, admits a purely algebraic description of its homotopy category as a certain derived categ ory. In this talk\, I'll describe joint work with Irakli Patchkoria in whi ch we prove Franke's conjecture\, subsuming and improving on virtually all known algebraicity results for stable infinity-categories.\n LOCATION:https://researchseminars.org/talk/MITTop/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Oscar Randal-Williams (University of Oxford) DTSTART:20200914T203000Z DTEND:20200914T213000Z DTSTAMP:20260422T212708Z UID:MITTop/20 DESCRIPTION:Title: Diffeomorphisms of discs\nby Oscar Randal-Williams (University of Oxfo rd) as part of MIT topology seminar\n\n\nAbstract\nIn dimensions $n \\neq 4$ the difference between groups of diffeomorphisms and of\nhomeomorphisms of an $n$-manifold $M$ is governed by an $h$-principle\, meaning that it reduces to understanding these groups for $M=\\mathbb{R}^n$. The group of diffeomorphisms is simple\, by linearising it is equivalent to $O(n)$\, bu t the group $Top(n)$ of homeomorphisms of $\\mathbb{R}^n$ has little struc ture and is difficult to grasp. It is profitable to instead consider the $ n$-disc $M=D^n$\, because the group of homeomorphisms of a disc (fixing th e boundary) is\ncontractible by Alexander's trick: this removes homeomorph isms from the picture\nentirely\, and makes the problem one purely within differential topology. I will\nexplain some of the history of this problem \, as well as recent work with A. Kupers in this direction.\n LOCATION:https://researchseminars.org/talk/MITTop/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Amnon Neeman (Australian National University) DTSTART:20201109T213000Z DTEND:20201109T223000Z DTSTAMP:20260422T212708Z UID:MITTop/21 DESCRIPTION:Title: A counterexample to conjectures in negative K-theory\nby Amnon Neeman (Australian National University) as part of MIT topology seminar\n\n\nAbst ract\nIn a 2006 article Schlichting conjectured that the negative K-theory of any abelian category must vanish. And in a 2019 article Antieau\, Gepn er and Heller generalized\, conjecturing that the negative K-theory of any infinity-category with a bounded t-structure must vanish.\n\nWe will revi ew the history\, explain why both conjectures are plausible\, and then ske tch a counterexample disproving both.\n LOCATION:https://researchseminars.org/talk/MITTop/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Speirs (Harvard) DTSTART:20201130T213000Z DTEND:20201130T223000Z DTSTAMP:20260422T212708Z UID:MITTop/22 DESCRIPTION:Title: Bass' NK-groups and arithmetic invariants\nby Martin Speirs (Harvard) as part of MIT topology seminar\n\n\nAbstract\nIn the 1970s Quillen proved that algebraic K-theory is homotopy invariant for a\nregular noetherian b ase. For a non-regular base ring this is not true. Bass\ndefined the NK-gr oups in order to study the failure of homotopy invariance in\nK-theory. In general these groups are not well understood\, though they have many\nint eresting properties. Ten years ago\, Cortiñas\, Haesemeyer\, Walker and W eibel\nused cdh-descent methods to understand the NK-groups when the input is rational.\nIn this talk I will explain parts of their work and discuss ongoing work with\nElden Elmanto where we aim to extend their methods to the mixed characteristic\nsetting.\n LOCATION:https://researchseminars.org/talk/MITTop/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Hahn (MIT) DTSTART:20201207T213000Z DTEND:20201207T223000Z DTSTAMP:20260422T212708Z UID:MITTop/23 DESCRIPTION:Title: Redshift for truncated Brown-Peterson spectra\nby Jeremy Hahn (MIT) as part of MIT topology seminar\n\n\nAbstract\nAusoni and Rognes calculated that K(ku) has chromatic height 2\, at least at primes larger than 3.\nThe ir redshift philosophy more generally suggests that the algebraic K-theory of a height n ring spectrum should have height n+1.\nI will explain work\ , joint with Dylan Wilson\, in which we equip BP(n) with an E_3-BP-algebra structure for all primes p and heights n.\nThe algebraic K-theory of this E_3 ring has chromatic height n+1\, giving an example of redshift at arbi trary height.\nTo show the ideas I may present quick proofs\, at the prime 2\, of the facts that K(ku) is height 2 and K(tmf) is height 3.\n LOCATION:https://researchseminars.org/talk/MITTop/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomer Schlank (Hebrew University) DTSTART:20210222T213000Z DTEND:20210222T223000Z DTSTAMP:20260422T212708Z UID:MITTop/24 DESCRIPTION:Title: Cyclotomic Galois extensions in the chromatic homotopy\nby Tomer Schla nk (Hebrew University) as part of MIT topology seminar\n\n\nAbstract\nThe chromatic approach to stable homotopy theory is 'divide and conquer'. That is\, questions about spectra are studies through various localizations th at isolate pure height phenomena and then are put back together. For each height n\, there are two main candidates for pure height localization. The first is the generally more accessible K(n)-localization and the second i s the closely related T(n)-localization. It is an open problem whether the two families of localizations coincide.\n\nOne of the main reasons that t he K(n)-local category is more amenable to computations is the existence o f well understood Galois extensions of the K(n)-local sphere.\n\nIn the ta lk\, I will present a generalization\, based on ambidexterity\, of the cla ssical theory of cyclotomic extensions\, suitable for producing non-trivia l Galois extensions in the T(n)-local and K(n)-local context. This constru ction gives a new family of Galois extensions of the T(n)-local sphere and allows to lift the well known maximal abelian extension of the K(n)-local sphere to the T(n)-local world.\n\nI will then describe some applications \, including the study of the T(n)-local Picard group\, a chromatic versio n of the Kummer theory\, and interaction with algebraic K-theory.\n\nThis is a joint project with Shachar Carmeli and Lior Yanovski.\n LOCATION:https://researchseminars.org/talk/MITTop/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Achim Krause (University of Münster) DTSTART:20210301T213000Z DTEND:20210301T223000Z DTSTAMP:20260422T212708Z UID:MITTop/25 DESCRIPTION:Title: Title to be announced\nby Achim Krause (University of Münster) as par t of MIT topology seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MITTop/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Najib Idrissi (IMJ-PRG) DTSTART:20210315T203000Z DTEND:20210315T213000Z DTSTAMP:20260422T212708Z UID:MITTop/26 DESCRIPTION:Title: Configuration spaces of surfaces\nby Najib Idrissi (IMJ-PRG) as part o f MIT topology seminar\n\n\nAbstract\nFramed configuration spaces of a sur face form a right module over the framed little disks operad. This rich al gebraic structure has important consequences\, for example for the computa tions of manifold calculus or factorization homology. Determining the homo topy type of this operadic right module remains however a difficult task. In this talk\, I will explain how to compute the rational homotopy type fo r oriented compact surfaces. The end result is a finite-dimensional purely combinatorial model. The proof involves several ingredients: Kontsevich ’s formality\, Tamarkin’s formality\, and the cyclic formality of the framed little disks operad. (Joint work with Ricardo Campos and Thomas Wil lwacher.)\n LOCATION:https://researchseminars.org/talk/MITTop/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Dylan Wilson (Harvard University) DTSTART:20210329T203000Z DTEND:20210329T213000Z DTSTAMP:20260422T212708Z UID:MITTop/27 DESCRIPTION:Title: Variations on the theme of Lichtenbaum-Quillen\nby Dylan Wilson (Harva rd University) as part of MIT topology seminar\n\n\nAbstract\nIn recent wo rk with Jeremy Hahn\, we established a higher chromatic version of the Lic htenbaum-Quillen conjecture for truncated Brown-Peterson spectra. This tal k will explore some questions raised by the proof\, and indicate some curr ent and future lines of investigation. Some of what we will discuss is als o joint with Akhil Mathew.\n LOCATION:https://researchseminars.org/talk/MITTop/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Nir Gadish (MIT) DTSTART:20210405T203000Z DTEND:20210405T213000Z DTSTAMP:20260422T212708Z UID:MITTop/28 DESCRIPTION:Title: Möbius inversion in hömotopy theory\nby Nir Gadish (MIT) as part of MIT topology seminar\n\n\nAbstract\nMöbius inversion is classically a pro cedure in number theory that inverts summation of functions over the divis ors of an integer. A similar construction is possible for every locally fi nite poset\, and is governed by a so called Möbius function encoding the combinatorics. In 1936 Hall observed that the values of the Möbius functi on are Euler characteristics of intervals in the poset\, suggesting a homo topy theoretic context for the inversion. In this talk we will discuss a f unctorial 'space-level' realization of Möbius inversion for diagrams taki ng values in a pointed cocomplete infinity-category. The role of the Möbi us function will be played by hömotopy types whose reduced Euler characte ristics are the classical values\, and inversion will hold up to extension s (think inclusion-exclusion but with the alternating signs replaced by ev en/odd spheres).\n\nThis provides a uniform perspective to many constructi ons in topology and algebra. Notable examples that I hope to mention inclu de handle decompositions\, Koszul resolutions\, and filtrations of configu ration spaces.\n LOCATION:https://researchseminars.org/talk/MITTop/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhulin Li (MIT) DTSTART:20210412T203000Z DTEND:20210412T213000Z DTSTAMP:20260422T212708Z UID:MITTop/29 DESCRIPTION:Title: Unstable modules with only the top k Steenrod operations\nby Zhulin Li (MIT) as part of MIT topology seminar\n\n\nAbstract\nIn this talk\, I wil l introduce unstable modules with only the top k Steenrod operations at th e prime 2. I'll show that they have projective dimension at most k. Then I 'll establish forgetful functors\, suspension functors\, loop functors and Frobenius functors between such modules. The forgetful functors induce an inverse system of Ext groups\, and the inverse system stabilizes when the covariant module is bounded above. In addition\, I will talk about a gene ralization of the Lambda algebra which computes the Ext group from such mo dules to suspensions of the base field.\n LOCATION:https://researchseminars.org/talk/MITTop/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Andy Senger (MIT) DTSTART:20210426T203000Z DTEND:20210426T213000Z DTSTAMP:20260422T212708Z UID:MITTop/30 DESCRIPTION:Title: Multiplicative structures on Brown-Peterson spectra at odd primes\nby Andy Senger (MIT) as part of MIT topology seminar\n\n\nAbstract\nWe show t hat the odd-primary Brown-Peterson spectrum does not admit the structure o f an E_{2(p^2+2)} ring spectrum and that there can be no map MU–>BP of E _{2p+3} ring spectra at any prime. This extends results of Lawson at the p rime 2.\n LOCATION:https://researchseminars.org/talk/MITTop/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Haine (MIT) DTSTART:20210503T203000Z DTEND:20210503T213000Z DTSTAMP:20260422T212708Z UID:MITTop/31 DESCRIPTION:Title: On the homotopy theory of stratified spaces\nby Peter Haine (MIT) as p art of MIT topology seminar\n\n\nAbstract\nA natural question arises when working with intersection cohomology and other stratified invariants of si ngular manifolds: what is the correct stable homotopy theory for these inv ariants to live in? But before answering that question one first has to id entify the correct unstable homotopy theory of stratified spaces. The exit -path category construction of MacPherson\, Treumann\, and Lurie provides functor from suitably nice stratified topological spaces to “abstract st ratified homotopy types” — ∞-categories with a conservative functor to a poset. Work of Ayala–Francis–Rozenblyum even shows that their con ically smooth stratified topological spaces embed into the ∞-category of abstract stratified homotopy types. In this talk\, we explain some of our work which goes further and produces an equivalence between the homotopy theory of all stratified topological spaces and these abstract stratified homotopy types.\n LOCATION:https://researchseminars.org/talk/MITTop/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Foling Zou (University of Michigan) DTSTART:20210510T203000Z DTEND:20210510T213000Z DTSTAMP:20260422T212708Z UID:MITTop/32 DESCRIPTION:Title: Nonabelian Poincare duality theorem and equivariant factorization homology of Thom spectra\nby Foling Zou (University of Michigan) as part of MI T topology seminar\n\n\nAbstract\nThe factorization homology are invariant s of n-dimensional manifolds with some fixed tangential structures that ta ke coefficients in suitable $\\mathbb{E}_n$-algebras. I will give a defini tion for the equivariant factorization homology of a framed manifold for a finite group G via a monadic bar construction following Miller-Kupers. I will also talk about the unital variant of symmetric sequences that is und erneath this construction. Then I will talk about the equivariant nonabeli an Poincare duality theorem in this case and the equivariant factorization homology on equivariant spheres for certain Thom spectra. This is joint w ith Asaf Horev\, Inbar Klang\, Peter May and Ruoqi Zhang.\n LOCATION:https://researchseminars.org/talk/MITTop/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Elden Elmanto (Harvard University) DTSTART:20210517T203000Z DTEND:20210517T213000Z DTSTAMP:20260422T212708Z UID:MITTop/33 DESCRIPTION:Title: Trace methods for algebraic stacks.\nby Elden Elmanto (Harvard Univers ity) as part of MIT topology seminar\n\n\nAbstract\nWe extend the Dundas-G oodwillie-McCarthy theorem concerning the fiber of the cyclotomic trace ma p from K theory to topological cyclic homology\, to the context of stable categories. Our main tool is Bondarko's theory of weight structures. Appli cations include a new proof of cdh-descent for homotopy K-theory of stacks (Hoyois-Krishna) and new cases of Blanc's lattice conjecture in noncommut ative Hodge theory (ala Katzarkov-Kontsevich-Pantev). Time permitting\, I will speak about vistas\, including the (equivariant) K-theory of the equi variant sphere and p-adic Hodge theory for stacks.\n\nThis is all joint wo rk with Vova Sosnilo and partly based on https://arxiv.org/abs/2010.09155\ n LOCATION:https://researchseminars.org/talk/MITTop/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Kirsten Wickelgren (Duke) DTSTART:20210322T203000Z DTEND:20210322T213000Z DTSTAMP:20260422T212708Z UID:MITTop/34 DESCRIPTION:Title: An excess intersection formula\nby Kirsten Wickelgren (Duke) as part o f MIT topology seminar\n\n\nAbstract\nOne expects the intersection of a d and n-d dimensional subscheme or submanifold of an n-dimensional one to be 0 dimensional. When this is not the case\, such intersections are often c alled excess intersections\, and arise when considering questions such as 'How many conics are tangent to 5 conics in the plane?' We consider cohomo logy classes in oriented Chow and Hermitian K-theory associated to excess intersections\, and use some recent duality results of Eisenbud and Ulrich to give an excess intersection formula. We compute some examples giving a rithmetic refinements of counts classically valid only over algebraically closed fields. This is joint work with Tom Bachmann.\n LOCATION:https://researchseminars.org/talk/MITTop/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Guozhen Wang (Shanghai Center for Mathematical Sciences) DTSTART:20210705T140000Z DTEND:20210705T150000Z DTSTAMP:20260422T212708Z UID:MITTop/35 DESCRIPTION:Title: Topological cyclic homology of local fields\nby Guozhen Wang (Shanghai Center for Mathematical Sciences) as part of MIT topology seminar\n\n\nAb stract\nWe introduce a new method for computing topological cyclic homolog y of locally complete intersections over p-adic intergers\, by using relat ive hochschild homology and resolving the base ring spectrum with an Adams reslolution. Using the Nygaard filtration on the E1-term\, we can constru ct algebraic Tate and algebraic homotopy fixed points spectral sequences\, which are algebraic and catpture lots of informations in the Tate and hom otopy fixed points spectral sequences computing TP and TC^{-1}. Using this method\, we can give a uniform way of computing topological cyclic homolo gy of local fields of mixed characteristic.\n LOCATION:https://researchseminars.org/talk/MITTop/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Land (University of Copenhagen) DTSTART:20210712T140000Z DTEND:20210712T150000Z DTSTAMP:20260422T212708Z UID:MITTop/36 DESCRIPTION:Title: Grothendieck—Witt theory of Dedekind rings and the stable cohomology of orthogonal and symplectic groups over Z\nby Markus Land (University of Copenhagen) as part of MIT topology seminar\n\n\nAbstract\nI will first g ive a brief overview of how one can understand classical Grothendieck—Wi tt theories of rings in terms of K-theoretic and L-theoretic pieces. Using this\, I will explain how to determine various Grothendieck—Witt theori es\, in particular of Dedekind rings. As further application of these resu lts\, I will then give a calculation of the stable cohomology of orthogona l and symplectic groups over the integers focussing on the mod 2 cohomolog y.\n\n This is all based on joint work with Calmès\, Dotto\, Harpa z\, Hebestreit\, Moi\, Nardin\, Nikolaus\, and Steimle\, and Hebestreit an d Nikolaus.\n LOCATION:https://researchseminars.org/talk/MITTop/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Shachar Carmeli (Weizmann Institute of Science) DTSTART:20210719T140000Z DTEND:20210719T150000Z DTSTAMP:20260422T212708Z UID:MITTop/37 DESCRIPTION:Title: Higher semiadditivity and the K(1)-local sphere\nby Shachar Carmeli (W eizmann Institute of Science) as part of MIT topology seminar\n\n\nAbstrac t\nHigher semiadditivity is a property of an infinity-category that allows \, in particular\, for the summation of families of morphisms between obje cts parametrized by pi-finite spaces.\n\nHopkins and Lurie showed that the K(n)-localizations of the infinity category of spectra are higher semiadd itive. Consequently\, by a work of Harpaz\, the mapping objects in these i nfinity-categories admit the rich structure of higher commutative monoids. \nWhile many abstract properties of these higher commutative monoids are k nown\, not many explicit computations of them have been carried out so far .\n\nIn my talk\, I will present a work in progress\, joint with Allen Yua n\, which aims to completely determine this higher commutative monoid stru cture of the K(1)-local sphere. Specifically\, I will show how to use high er semiadditive versions of algebraic K-theory and Grothendieck-Witt theor y to compute the summation maps along groupoids for the K(1)-local sphere. At the prime 2\, this allows us to realize some non-trivial classes in i ts homotopy groups as semiadditive cardinalities of pi-finite spaces\, and to compute explicitly certain power operations that arise from the higher semiadditivity.\n LOCATION:https://researchseminars.org/talk/MITTop/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Lior Yanovski (Max Planck Institute) DTSTART:20210823T140000Z DTEND:20210823T150000Z DTSTAMP:20260422T212708Z UID:MITTop/38 DESCRIPTION:Title: The chromatic discrete Fourier transform\nby Lior Yanovski (Max Planck Institute) as part of MIT topology seminar\n\n\nAbstract\nThe classical d iscrete Fourier transform can be thought of as an isomorphism of rings bet ween the complex group algebra of a finite abelian group A and the algebra of functions on its Pontyagin dual. Hopkins and Lurie have proved an anal ogous result in the chromatic world\, where the field of complex numbers i s replaced by the Lubin-Tate spectrum E_n\, the finite abelian group A is replaced by a suitably finite p-power torsion Z-module spectrum\, and the Pontryagin dual is modified by an n-fold suspension. From this\, they dedu ce a number of structural properties of the infinity-category of K(n)-loca l spectra\, such as affineness and Eilenberg-Moore type formulas for pi-fi nite spaces. In this talk\, I will present a joint work with Barthel\, Car meli\, and Sclank\, in which we develop the notion of a `higher Discrete F ourier transform' for general higher semiadditive infinity-categories. Thi s allows us\, among other things\, to extend the above results of Hopkins and Lurie to the T(n)-local setting. Furthermore\, we study the interactio n of Fourier transforms with categorification suggesting a close relations hip to chromatic redshift phenomena. Finally\, by replacing Pontryagin dua lity with Brown-Comenetz duality\, we can contemplate the notion of Fourie r transform for more general pi-finite spectra than Z-modules\, leading to questions intimately related to the behavior of the `discrepancy spectru m'.\n LOCATION:https://researchseminars.org/talk/MITTop/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Joana Cirici (Universitat de Barcelona) DTSTART:20211108T213000Z DTEND:20211108T223000Z DTSTAMP:20260422T212708Z UID:MITTop/39 DESCRIPTION:Title: Title to be announced.\nby Joana Cirici (Universitat de Barcelona) as part of MIT topology seminar\n\n\nAbstract\nAbstract to be shared.\n LOCATION:https://researchseminars.org/talk/MITTop/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Arpon Raksit (MIT) DTSTART:20211115T213000Z DTEND:20211115T223000Z DTSTAMP:20260422T212708Z UID:MITTop/40 DESCRIPTION:Title: Canonical lifts and spectral algebraic geometry\nby Arpon Raksit (MIT) as part of MIT topology seminar\n\n\nAbstract\nLet X be an elliptic curve over a perfect field k of positive characteristic. Serre–Tate studied t he deformation theory of such X\, and one of their discoveries was that wh en X is ordinary\, it admits a canonical lifting to the ring of Witt vecto rs W(k) (with some special features). In this talk\, I'll discuss a connec tion between this phenomenon and properties of the moduli of elliptic curv es in spectral algebraic geometry introduced by Lurie.\n LOCATION:https://researchseminars.org/talk/MITTop/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Hana Kong (IAS) DTSTART:20211129T213000Z DTEND:20211129T223000Z DTSTAMP:20260422T212708Z UID:MITTop/41 DESCRIPTION:Title: The homotopy of motivic image-of-j spectrum\nby Hana Kong (IAS) as par t of MIT topology seminar\n\nLecture held in Room: 2-131 in the MIT Simons Building.\n\nAbstract\nBachmann–Hopkins defines the motivic 'image-of-j ' spectrum over base fields with characteristic not 2. In this talk\, I wi ll talk about the effective slice computation of this spectrum over the re al numbers. Analogous to the classical story\, the result captures a regul ar pattern that appears in the R-motivic stable stems. This is joint work with Eva Belmont and Dan Isaksen.\n LOCATION:https://researchseminars.org/talk/MITTop/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Dylan Wilson (Harvard) DTSTART:20211206T213000Z DTEND:20211206T223000Z DTSTAMP:20260422T212708Z UID:MITTop/42 DESCRIPTION:Title: Title to be announced.\nby Dylan Wilson (Harvard) as part of MIT topol ogy seminar\n\nLecture held in Room: 2-131 in the MIT Simons Building.\n\n Abstract\nabstract to be shared soon.\n LOCATION:https://researchseminars.org/talk/MITTop/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Elden Elmanto (Harvard University) DTSTART:20211122T213000Z DTEND:20211122T223000Z DTSTAMP:20260422T212708Z UID:MITTop/43 DESCRIPTION:Title: Motivic cohomology reimagined\nby Elden Elmanto (Harvard University) a s part of MIT topology seminar\n\n\nAbstract\nBeilinson\, Macpherson and S chechtman asked us to imagine a world where topological K-theory was first defined before singular cohomology. How would one invent the latter? This question has been influential to various approaches to motivic cohomology of smooth varieties with its relationship to K-theory\, serving a 'design principle.' I will explain an extension of this idea to define a version of motivic cohomology of singular schemes. The engine behind it is the Bha tt-Morrow-Scholze prismatic sheaves.\n\nThis is all joint work with Tom Ba chmann and Matthew Morrow.\n LOCATION:https://researchseminars.org/talk/MITTop/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Pstrągowski (Harvard University) DTSTART:20220328T203000Z DTEND:20220328T213000Z DTSTAMP:20260422T212708Z UID:MITTop/44 DESCRIPTION:Title: Quivers and the Adams Spectral Sequence\nby Piotr Pstrągowski (Harvar d University) as part of MIT topology seminar\n\nLecture held in Room 2-13 1 in the Simons building.\n\nAbstract\nAssociated to each homology theory we have an Adams spectral sequence computing stable homotopy classes of ma ps. Under flatness assumptions\, the E2-term can be identified with cohomo logy of a certain Hopf algebroid\, giving the spectral sequence its comput ational power. Unfortunately\, this identification fails in many important examples\, such as integral homology or connective Morava K-theory\, maki ng these spectral sequences mysterious and hard to calculate with. In this talk\, I will describe a novel method of identifying these E2-terms in te rms of cohomology in representations of certain quivers. This is based on joint work with Burklund.\n\nTo add this to your calendar\, the ics file f or this seminar is here:\nhttp://math.mit.edu/topology/topology_seminar.ic s\n LOCATION:https://researchseminars.org/talk/MITTop/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Sulyma (Brown University) DTSTART:20220404T203000Z DTEND:20220404T213000Z DTSTAMP:20260422T212708Z UID:MITTop/45 DESCRIPTION:Title: Floor Homotopy Theory\nby Yuri Sulyma (Brown University) as part of MI T topology seminar\n\nLecture held in Room 2-131 in the Simons Building.\n \nAbstract\nOne perspective on homotopy theory is that it is an enhanced v ersion of arithmetic which remembers combinatorics and symmetry. I will de monstrate this philosophy concretely in the case of the floor and ceiling functions from arithmetic\, by explaining several situations where these a ppear: K-theory of truncated polynomial algebras\; Legendre's formula and its q-analogue\; hyper-representation-graded TR\; and equivariant homotopy theory. To understand how these examples are related\, I will show how to construct a Tambara functor out of a prism\, and discuss a conjectural th eory of G-crystalline/G-de Rham cohomology generalizing q-crystalline coho mology and the q-de Rham complex.\n LOCATION:https://researchseminars.org/talk/MITTop/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Araminta Amabel (MIT) DTSTART:20220411T203000Z DTEND:20220411T213000Z DTSTAMP:20260422T212708Z UID:MITTop/46 DESCRIPTION:Title: Title to be shared\nby Araminta Amabel (MIT) as part of MIT topology s eminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MITTop/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Burklund (MIT) DTSTART:20220425T203000Z DTEND:20220425T213000Z DTSTAMP:20260422T212708Z UID:MITTop/47 DESCRIPTION:Title: Title to be shared\nby Robert Burklund (MIT) as part of MIT topology s eminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/MITTop/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Yajit Jain (Brown University) DTSTART:20220502T203000Z DTEND:20220502T213000Z DTSTAMP:20260422T212708Z UID:MITTop/48 DESCRIPTION:Title: Topologically Trivial Families of Smooth h-Cobordisms\nby Yajit Jain ( Brown University) as part of MIT topology seminar\n\n\nAbstract\nAfter usi ng smoothing theory to introduce a notion of exotic smooth structures on m anifold bundles\, we will discuss an equivalent class of objects: smooth b undles of h-cobordisms with a topological trivialization. Using work of Dw yer\, Weiss\, and Williams\, we will associate to such families an invaria nt called the smooth structure class\, which is closely related to the hig her Franz-Reidemeister torsion of Igusa and Klein. We will illustrate two proofs of a duality theorem for the smooth structure class. This theorem g eneralizes Milnor's duality theorem for Whitehead torsion. A consequence o f this result is the rigidity conjecture of Goette and Igusa\, which state s that\, after rationalizing\, stable exotic smoothings of manifold bundle s with closed even dimensional fibers do not exist.\n LOCATION:https://researchseminars.org/talk/MITTop/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Noah Riggenbach (Northwestern University) DTSTART:20220509T203000Z DTEND:20220509T213000Z DTSTAMP:20260422T212708Z UID:MITTop/49 DESCRIPTION:Title: NTC of Perfectoid Rings\nby Noah Riggenbach (Northwestern University) as part of MIT topology seminar\n\nLecture held in Room: 2-131 in the MIT Simons Building.\n\nAbstract\nIn this talk I will discuss my recent comput ation of the NTC groups of perfectoid rings which have a system of pth pow er roots of unity and thus the KK-groups of the p-completed affine line  R⟨x⟩R⟨x⟩ over these rings relative to the ideal (x)(x). This inc ludes all perfect fields of positive characteristic\, for which these grou ps vanish in non-negative degrees. This class of rings also contains many mixed characteristic rings\, and perhaps surprisingly while the even nonne gative groups will still vanish\, the odd groups will not.\n LOCATION:https://researchseminars.org/talk/MITTop/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Akhil Mathew (University of Chicago) DTSTART:20220919T190000Z DTEND:20220919T200000Z DTSTAMP:20260422T212708Z UID:MITTop/50 DESCRIPTION:Title: Syntomic complexes of regular rings\nby Akhil Mathew (University of Ch icago) as part of MIT topology seminar\n\nLecture held in Room 2-131.\n\nA bstract\nSyntomic complexes are a form of p-adic motivic cohomology that f ilter p-adic \\’etale K-theory (or topological cyclic homology)\, and wh ich are defined in terms of prismatic cohomology. I will explain a descrip tion of the syntomic complexes of p-torsionfree regular rings\, based on a mixed characteristic analog of the Cartier isomorphism\, closely related to the Segal conjecture for THH. (Joint with Bhargav Bhatt.)\n\nSpecial Se minar Time at 3pm!\n\nThe seminar will meet at 4:30 on Mondays in 2-131 un less otherwise noted.\n\nClick here to add this seminar to your google cal endar. If you use a different calendar program\, the ics file for this sem inar is here:\nhttp://math.mit.edu/topology/topology_seminar.ics\n LOCATION:https://researchseminars.org/talk/MITTop/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Arpon Raksit (MIT) DTSTART:20220926T203000Z DTEND:20220926T213000Z DTSTAMP:20260422T212708Z UID:MITTop/51 DESCRIPTION:Title: The Even Filtration\nby Arpon Raksit (MIT) as part of MIT topology sem inar\n\nLecture held in Room 2 - 131.\n\nAbstract\nThis talk will be about joint work with Jeremy Hahn and Dylan Wilson in which we define a filtrat ion on an arbitrary commutative ring spectrum that we call the "even filtr ation". I'll introduce the definition\, the one method we've come up with for analyzing it\, and its relation to other filtrations of interest\, in particular motivic filtrations on topological Hochschild homology.\n LOCATION:https://researchseminars.org/talk/MITTop/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Kuhn (University of Virginia) DTSTART:20221003T203000Z DTEND:20221003T213000Z DTSTAMP:20260422T212708Z UID:MITTop/52 DESCRIPTION:Title: Chromatic Fixed Point Theory\nby Nick Kuhn (University of Virginia) as part of MIT topology seminar\n\nLecture held in Room 2-131 in the Simons building.\n\nAbstract\n\\noindent The study of the action of a finite p-gr oup G on a finite G-CW complex X is one of the oldest topics in algebraic topology. In the late 1930's\, P. A. Smith proved that if X is mod p acycl ic\, then so is XG\, its subspace of fixed points. A related theorem of Ed Floyd from the early 1950's says that the dimension of the mod p homology of X will bound the dimension of the mod p homology of XG.\n\n\\smallskip \n\nThe study of the Balmer spectrum of the homotopy category of G-spectra has lead to the problem of identifying "chromatic" variants of Smith's th eorem\, with mod p homology replaced by the Morava K-theories (at the prim e p). One such chromatic Smith theorem is proved by Barthel et.al.: if G i s a cyclic p-group and X is K(n) acyclic\, then XG is K(n−1) acyclic (an d this answers questions like this for all abelian p-groups).\n\n\\smallsk ip\n\nIn work with Chris Lloyd\, we have been able to show that a chromati c analogue of Floyd's theorem is true whenever a chromatic Smith theorem h olds. For example\, if G is a cyclic p-group\, then the dimension over K(n )∗ of K(n)∗(X) will bound the dimension over K(n−1)∗ of K(n−1) ∗(XG).\n\n\\smallskip\n\nThe proof that chromatic Smith theorems imply t he stronger chromatic Floyd theorems uses the representation theory of the symmetric groups.\n\n\\smallskip\n\nThese chromatic Floyd theorems open t he door for many applications. We have been able to resolve open questions involving the Balmer spectrum for the extraspecial 2-groups. In a differe nt direction\, at the prime 2\, we can show quick collapsing of the AHSS c omputing the Morava K-theory of some real Grassmanians: this is a non-equi variant result.\n\n\\smallskip\n\nIn my talk\, I'll try to give an overvie w of some of this.\n LOCATION:https://researchseminars.org/talk/MITTop/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Rivera (Purdue University) DTSTART:20221017T140000Z DTEND:20221017T150000Z DTSTAMP:20260422T212708Z UID:MITTop/53 DESCRIPTION:Title: Simplicial coalgebras under three different notions of weak equivalence\nby Manuel Rivera (Purdue University) as part of MIT topology seminar\n\ n\nAbstract\n\\noindent Motivated by constructing algebraic models for hom otopy types\, I will discuss three different homotopy theories on the cate gory of simplicial cocommutative coalgebras corresponding to the following notions of weak equivalence:\n\n\\vspace{2ex}\n\n\\begin{itemize}\n\n\\it em 1. maps of simplicial coalgebras which become quasi-isomorphisms of dif ferential graded (dg) coalgebras after applying the normalized chains func tor\n\n\\item 2. maps of simplicial coalgebras which become quasi-isomorph isms of dg algebras after applying the normalized chains functor followed by the dg cobar construction\, and\n\n\\item 3. maps of simplicial coalgeb ras which become quasi-isomorphisms of dg algebras after applying a locali zed version of the dg cobar construction.\n\n\\end{itemize}\n\n\\vspace{2e x}\n\n\\noindent Notion (1) was used by Goerss to provide a fully-faithful model for spaces up to F-homology equivalence\, for a F an algebraically closed field. I will explain how (2)\, which is drawn from dg Koszul duali ty theory\, corresponds to a linearized version of the notion of categoric al equivalence between simplicial sets as used in the theory of quasi-cate gories. I will also explain how (3) leads to a fully-faithful model for th e homotopy theory of simplicial sets considered up to maps that induce iso morphisms on fundamental groups and on the F-homology of the universal cov ers\, for F an algebraically closed field. One of the key points is a sort of homological formulation of the fundamental group. This is based on joi nt work with G. Raptis and also on work with F. Wierstra and M. Zeinalian. \n LOCATION:https://researchseminars.org/talk/MITTop/53/ END:VEVENT END:VCALENDAR