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:20260404T094119Z
UID:MITTop/1
DESCRIPTION:Title: An orientation map for height $p−1$ real $E$ theory\nby Hood C
hatham (MIT) as part of MIT topology seminar\n\n\nAbstract\nLet $p$ be an
odd prime 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 $X$ ha
s algebraic $\\operatorname{EO}$ theory if the splitting of $K_*(X)$ as an
$K_*[C_p]$ module lifts to a topological splitting of $\\operatorname{EO}
\\wedge X$. We develop criteria to show that a spectrum has algebraic $\\
operatorname{EO}$ theory\, in particular showing that any connnective spec
trum with mod $p$ homology concentrated in degrees $2k(p−1)$ has algebra
ic $\\operatorname{EO}$ theory. As an application\, we answer a question p
osed by Hovey and Ravenel by producing a unital orientation $MW_{4p−4} \
\to \\operatorname{EO}$ analogous to the $MSU$ orientation of $KO$ at $p=2
$ where $MW_{4p−4}$ is the Thom spectrum of the $(4p−4)$-connective Wi
lson space.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Campbell (Duke)
DTSTART:20200413T203000Z
DTEND:20200413T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/2
DESCRIPTION:Title: Homotopy theory and Hilbert’s third problem\nby Jonathan Campb
ell (Duke) as part of MIT topology seminar\n\n\nAbstract\nIn this talk I'l
l explain how one might attack Hilbert's Generalized Third Problem via hom
otopy theory\, and describe recent progress in this direction. Two $n$-dim
ensional polytopes\, $P$\, $Q$ are said to be scissors congruent if one ca
n cut $P$ along a finite number of hyperplanes\, and re-assemble the piece
s into $Q$. The scissors congruence problem\, aka Hilbert's Generalized Th
ird Problem\, asks: when can we do this? what obstructs this? In two dimen
sions\, two polygons are scissors congruent if and only if they have the s
ame area. In three dimensions\, there is volume and another invariant\, th
e Dehn Invariant. In higher dimensions\, very little is known — but the
problem is known to have deep connections to motives\, values of zeta func
tions\, the weight filtration in algebraic K-theory\, and regulator maps.
I'll give a leisurely introduction to this very classical problem\, and ex
plain some new results obtained via homotopy theoretic techniques. This is
joint work with Inna Zakharevich.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Ching (Amherst College)
DTSTART:20200427T203000Z
DTEND:20200427T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/3
DESCRIPTION:Title: Tangent ∞-categories and Goodwillie calculus\nby Michael Ching
(Amherst College) as part of MIT topology seminar\n\n\nAbstract\n(Joint w
ith Kristine 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 fra
mework which includes both this construction and the ordinary tangent bund
le functor on the category of smooth manifolds (as well as many other exam
ples). That framework is an extension to ∞-categories of the “tangent
categories” of Cockett and Cruttwell (based on earlier work of Rosický)
.\n\nThose authors and others have explored the extent to which various co
ncepts from differential geometry\, such as connections\, curvature and co
homology\, 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
Goodwillie’s notion of n-excisive functor can be recovered from the gen
eral notion of “n-jet” in a tangent category.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhouli Xu (MIT)
DTSTART:20200504T203000Z
DTEND:20200504T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/4
DESCRIPTION:Title: Stable stems and the Chow-Novikov t-structure in motivic stable homo
topy category\nby Zhouli Xu (MIT) as part of MIT topology seminar\n\n\
nAbstract\nIn this talk\, I will discuss recent progress on the computatio
n of classical stable homotopy groups of spheres\, and highlight some new
results regarding certain Adams differentials and their connections to the
Kervaire invariant classes. These computations use the Chow-Novikov t-str
ucture on the cellular motivic stable homotopy theory over C in an essenti
al 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 potential applications in computations.\n\nThis talk is based on seve
ral joint projects involving Tom Bachmann\, Robert Burklund\, Bogdan Gheor
ghe\, Dan Isak- sen\, Hana Jia Kong and Guozhen Wang.\n\nFor information\,
write: burklund@mit.edu\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tyler Lawson (University of Minnesota)
DTSTART:20200511T203000Z
DTEND:20200511T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/5
DESCRIPTION:Title: Obstruction theory for ring spectra\nby Tyler Lawson (University
of Minnesota) as part of MIT topology seminar\n\n\nAbstract\nI'll discuss
calculational methods for determining moduli of objects and maps between
$E_\\infty$ ring spectra\, and the relation to topological Andre-Quillen c
ohomology.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Yakerson (Regensburg University)
DTSTART:20200721T160000Z
DTEND:20200721T170000Z
DTSTAMP:20260404T094119Z
UID:MITTop/6
DESCRIPTION:Title: New Models for Motivic K-Theory Spectra\nby Maria Yakerson (Rege
nsburg University) as part of MIT topology seminar\n\n\nAbstract\nAlgebrai
c and hermitian K-theories of smooth schemes are generalized cohomology th
eories\, represented in the motivic stable homotopy category. In this tal
k\, we explain how to obtain new geometric models for the corresponding mo
tivic spectra\, based on the specific kinds of transfer maps that these co
homology theories acquire. As a surprising side-effect\, we compute the
motivic homotopy type of the Hilbert scheme of infinite affine space. Th
is is joint work with Marc Hoyois\, Jochim Jelisiejew\, Denis Nardin and B
urt Totaro.\n\nFor information\, write: adelayyz@mit.edu\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Clausen (Max Plank Institute)
DTSTART:20200728T160000Z
DTEND:20200728T170000Z
DTSTAMP:20260404T094119Z
UID:MITTop/7
DESCRIPTION:Title: The Linearization Hypothesis\nby Dustin Clausen (Max Plank Insti
tute) as part of MIT topology seminar\n\n\nAbstract\nLazard showed that th
e continuous group cohomology of a large class ofp-adic Lie groups\, with
p-adic coefficients\, satisfies Poincare duality. Analogously to the usual
Poincare duality of real manifolds\, there are orientability issues\, but
Lazard showed that the relevant orientation local system is completely de
termined by the adjoint representation of the group in an explicit manner\
, allowing for an easy analysis. This can be compared to how the orientat
ion local system on a real manifold is determined by the tangent bundle\,
a very useful "linearization" of the problem. Now\, there is an analogous
Poincare duality with spectrum coefficients both in the setting of p-adic
Lie groups and in the setting of real manifolds. In the latter case the
relevant orientation local system is still determined by the tangent bundl
e\; in fact it is the suspension spectrum of the associated sphere bundle\
, a statement known as Atiyah duality. In the former case\, there is a na
tural guess for how the orientation local system should still be determine
d by the adjoint representation. This has been highlighted by recent work
of Beaudry-Goerss-Hopkins-Stojanoska in their study of duality for tmf\,
and they dubbed this guess the "linearization hypothesis". Neither Lazard
's techniques nor the usual arguments for Atiyah duality can be used to at
tack the\nlinearization hypothesis. In this talk I will explain a proof o
f the linearization hypothesis\, whose main ingredients are a deformation
of any p-adic Lie group to its Lie algebra\, and a rather exotic "cospecia
lization map" which lets you use this deformation to jump from the Lie alg
ebra to the Lie group as if the deformation were parametrized by a unit in
terval\, even though it is only parametrized by a totally disconnected spa
ce.\n
LOCATION:https://stable.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:20260404T094119Z
UID:MITTop/8
DESCRIPTION:Title: Higher Brauer groups\nby Benjamin Antieau (University of Illinoi
s at Chicago and Northwestern University) as part of MIT topology seminar\
n\n\nAbstract\nI will give an introduction to the idea of higher Brauer gr
oups\, focusing on the "next" higher Brauer group\, consisting of Morita e
quivalence classes of certain Azumaya categories. The emphasis of the talk
will be on analogies\, examples\, calculations\, and open problems.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Nikolaus (Münster)
DTSTART:20200811T160000Z
DTEND:20200811T170000Z
DTSTAMP:20260404T094119Z
UID:MITTop/9
DESCRIPTION:Title: On Grothendieck--Witt theory of the integers.\nby Thomas Nikolau
s (Münster) as part of MIT topology seminar\n\n\nAbstract\nWe introduce t
he Grothendieck--Witt groups of the integers and the Grothendieck--Witt sp
ectrum of the integers. Then we explain how to compute these groups and th
e homotopy type of the spectrum using recent work on K-theory and L-theory
. If time permits we also explain how to resolve the homotopy limit proble
m for rings of integers in number fields and prove Karoubi's periodicity c
onjecure for arbitrart rings.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Hoyois (Regensburg University)
DTSTART:20200818T160000Z
DTEND:20200818T170000Z
DTSTAMP:20260404T094119Z
UID:MITTop/10
DESCRIPTION:Title: Milnor excision for motivic spectra\nby Marc Hoyois (Regensburg
University) as part of MIT topology seminar\n\n\nAbstract\nIt is a classi
cal result of Weibel that homotopy invariant algebraic\nK-theory satisfies
excision\, in the sense that for any ring A and ideal I ⊂ A\,\nthe fibe
r of KH(A) → KH(A/I) depends only on I as a nonunital ring. In joint\nw
ork with Elden Elmanto\, Ryomei Iwasa\, and Shane Kelly\, we show that thi
s is\ntrue more generally for any cohomology theory represented by a motiv
ic spectrum.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rune Haugseng (Norwegian University of Science and Technology)
DTSTART:20200825T160000Z
DTEND:20200825T170000Z
DTSTAMP:20260404T094119Z
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://stable.researchseminars.org/talk/MITTop/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Gepner (University of Illinois at Chicago)
DTSTART:20200921T203000Z
DTEND:20200921T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/12
DESCRIPTION:Title: Elliptic cohomology of the unitary group\nby David Gepner (Univ
ersity of Illinois at Chicago) as part of MIT topology seminar\n\n\nAbstra
ct\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 H
ilbert\nscheme of points of the associated derived elliptic curve. To this
end\, we will\nbegin with a discussion of (integral) equivariant elliptic
cohomology\, due to\nJacob Lurie\, using the formalism of orbispaces\, as
developed by myself and Andre\nHenriques. This is joint work with Lennart
Meier.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Regensburg University)
DTSTART:20200928T203000Z
DTEND:20200928T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/13
DESCRIPTION:Title: Derived cycle classes\nby Adeel Khan (Regensburg University) as
part of MIT topology seminar\n\n\nAbstract\nLet X be a smooth complex alg
ebraic variety. In contrast with the situation for the singular homology g
roups H_*(X)\, the construction of intersection products on the Chow group
s of X is subtle due to the comparative difficulty in dealing with non-tra
nsverse intersections. I will explain one way to deal with this problem by
considering cycle classes that come from derived algebraic geometry. In c
ombination with the algebraic analogue of Steenrod's problem on resolution
of singularities of homology classes (which holds by Hironaka)\, this yie
lds a new construction of cup products in Chow groups. Time permitting\, I
may also discuss how derived cycle classes arise in motivic homotopy theo
ry.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Campbell (Center for Communications Research La Jolla)
DTSTART:20201005T203000Z
DTEND:20201005T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/14
DESCRIPTION:Title: Homotopy Theory and Hilbert's Third Problem\nby Jonathan Campbe
ll (Center for Communications Research La Jolla) as part of MIT topology s
eminar\n\n\nAbstract\nIn this talk I'll explain how one might attack Hilbe
rt's Generalized Third\nProblem via homotopy theory\, and describe recent
progress in this direction. Two\nn-dimensional polytopes\, $P$\, $Q$ are s
aid to be scissors congruent if one can\ncut $P$ along a finite number of
hyperplanes\, and re-assemble the pieces into\n$Q$. The scissors congruenc
e problem\, aka Hilbert's Generalized Third Problem\,\nasks: when can we d
o this? What obstructs this? In two dimensions\, two polygons\nare scissor
s congruent if and only if they have the same area. In three\ndimensions\,
there is volume and another invariant\, the Dehn Invariant. In higher\ndi
mensions\, very little is known --- but the problem is known to have deep\
nconnections to motives\, values of zeta functions\, the weight filtration
in\nalgebraic K-theory\, and regulator maps. I'll give a leisurely introd
uction to\nthis very classical problem\, and explain some new results obta
ined via homotopy\ntheoretic techniques. This is all joint with Inna Zakh
arevich.\n\n\n\nAdd this seminar to your calendar : http://math.mit.edu/to
pology/topology_seminar.ics\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Knudsen (Northeastern University)
DTSTART:20201019T203000Z
DTEND:20201019T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/15
DESCRIPTION:Title: Smooth structures and embedding calculus\nby Ben Knudsen (North
eastern University) as part of MIT topology seminar\n\n\nAbstract\nWe ask
when embedding calculus can distinguish pairs of smooth\nmanifolds that ar
e homeomorphic but not diffeomorphic. We prove that\, in\ndimension 4\, th
e answer is “almost never.” In contrast\, we exhibit an infinite\nlist
of high-dimensional exotic spheres detected by embedding calculus. The\nf
ormer result implies that the algebraic topology of knot spaces is insensi
tive\nto smooth structure in dimension 4\, answering a question of Viro. T
he latter\nresult gives a partial answer to a question of Francis and hint
s at the\npossibility of a new classification of exotic spheres in terms o
f a stratified\nobstruction theory applied to compactified configuration s
paces. 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://stable.researchseminars.org/talk/MITTop/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcy Robertson (University of Melbourne)
DTSTART:20201026T203000Z
DTEND:20201026T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/16
DESCRIPTION:Title: Expansions\, completions and automorphisms of welded tangled foams<
/a>\nby Marcy Robertson (University of Melbourne) as part of MIT topology
seminar\n\n\nAbstract\nWelded tangles are knotted surfaces in $\\mathbb{R}
^4$. Bar-Natan and Dancso described a class of welded tangles which have
“foamed vertices” where one allows surfaces to merge and split. The re
sulting welded tangled foams carry an algebraic structure\, similar to the
planar algebras of Jones\, called a circuit algebra. In joint work with D
ancso and Halacheva we provide a one-to-one correspondence between circuit
algebras and a form of rigid tensor category called ``wheeled props.'' Th
is is a higher dimensional version of the well-known algebraic classificat
ion of planar algebras as certain pivotal categories.\n\n\nThis classifica
tion allows us to connect these ``welded tangled foams\,'' to the Kashiwar
a-Vergne conjecture in Lie theory. In work in progress\, we show that the
group of homotopy automorphisms of the (rational completion of) the wheele
d prop of welded foams is isomorphic to the group of symmetries KV\, which
acts on the solutions to the Kashiwara-Vergne conjecture. Moreover\, we e
xplain\nhow this approach illuminates the close relationship between the g
roup KV and the pro-unipotent Grothendieck--Teichmüller group.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Hausmann (Universität Bonn)
DTSTART:20200630T160000Z
DTEND:20200630T170000Z
DTSTAMP:20260404T094119Z
UID:MITTop/17
DESCRIPTION:Title: Global group laws and the equivariant Quillen theorem\nby Marku
s Hausmann (Universität Bonn) as part of MIT topology seminar\n\n\nAbstra
ct\nI will discuss an equivariant version of Quillen's theorem that the co
mplex bordism ring carries the universal formal group law\, both over a fi
xed abelian group and in a global equivariant setting.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnès Beaudry (University of Colorado Boulder)
DTSTART:20201116T213000Z
DTEND:20201116T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/18
DESCRIPTION:Title: Equivariant Morava K-Theories?\nby Agnès Beaudry (University o
f Colorado Boulder) as part of MIT topology seminar\n\n\nAbstract\nAt heig
ht $h=2^{n-1}m$\, the Morava stabilizer group contains a cyclic group $G$\
nof order $2^n$. In this talk\, I will present equivariant spectra that re
fine the\nclassical height $h$ Morava $K$-theories. These are obtained fro
m\n$G$-equivariant models of Lubin-Tate spectra which were constructed in
recent\njoint work with Hill-Shi-Zeng. I will present some preliminary re
sults and\nconjectures about their slice filtration and equivariant homoto
py groups and\ndiscuss how exotic transchromatic extensions lead to intere
sting differentials.\n\nThis is joint work with Hill-Shi-Zeng.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Pstragowski (Harvard)
DTSTART:20201102T213000Z
DTEND:20201102T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/19
DESCRIPTION:Title: Franke's algebraicity conjecture\nby Piotr Pstragowski (Harvard
) as part of MIT topology seminar\n\n\nAbstract\nIn 1996\, Jens Franke con
jectured that any stable infinity-category possessing an Adams spectral se
quence whose sparsity is greater than the homological dimension\, admits a
purely algebraic description of its homotopy category as a certain derive
d category. In this talk\, I'll describe joint work with Irakli Patchkoria
in which we prove Franke's conjecture\, subsuming and improving on virtua
lly all known algebraicity results for stable infinity-categories.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Randal-Williams (University of Oxford)
DTSTART:20200914T203000Z
DTEND:20200914T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/20
DESCRIPTION:Title: Diffeomorphisms of discs\nby Oscar Randal-Williams (University
of Oxford) as part of MIT topology seminar\n\n\nAbstract\nIn dimensions $n
\\neq 4$ the difference between groups of diffeomorphisms and of\nhomeomo
rphisms of an $n$-manifold $M$ is governed by an $h$-principle\, meaning t
hat it reduces to understanding these groups for $M=\\mathbb{R}^n$. The gr
oup of diffeomorphisms is simple\, by linearising it is equivalent to $O(n
)$\, but the group $Top(n)$ of homeomorphisms of $\\mathbb{R}^n$ has littl
e structure and is difficult to grasp. It is profitable to instead conside
r the $n$-disc $M=D^n$\, because the group of homeomorphisms of a disc (fi
xing the boundary) is\ncontractible by Alexander's trick: this removes hom
eomorphisms 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://stable.researchseminars.org/talk/MITTop/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Neeman (Australian National University)
DTSTART:20201109T213000Z
DTEND:20201109T223000Z
DTSTAMP:20260404T094119Z
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\nAbstract\nIn a 2006 article Schlichting conjectured that the negative K
-theory of any abelian category must vanish. And in a 2019 article Antieau
\, Gepner and Heller generalized\, conjecturing that the negative K-theory
of any infinity-category with a bounded t-structure must vanish.\n\nWe wi
ll review the history\, explain why both conjectures are plausible\, and t
hen sketch a counterexample disproving both.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Speirs (Harvard)
DTSTART:20201130T213000Z
DTEND:20201130T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/22
DESCRIPTION:Title: Bass' NK-groups and arithmetic invariants\nby Martin Speirs (Ha
rvard) as part of MIT topology seminar\n\n\nAbstract\nIn the 1970s Quillen
proved that algebraic K-theory is homotopy invariant for a\nregular noeth
erian base. For a non-regular base ring this is not true. Bass\ndefined th
e NK-groups in order to study the failure of homotopy invariance in\nK-the
ory. In general these groups are not well understood\, though they have ma
ny\ninteresting properties. Ten years ago\, Cortiñas\, Haesemeyer\, Walke
r and Weibel\nused cdh-descent methods to understand the NK-groups when th
e 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 meth
ods to the mixed characteristic\nsetting.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Hahn (MIT)
DTSTART:20201207T213000Z
DTEND:20201207T223000Z
DTSTAMP:20260404T094119Z
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 calc
ulated that K(ku) has chromatic height 2\, at least at primes larger than
3.\nTheir redshift philosophy more generally suggests that the algebraic K
-theory of a height n ring spectrum should have height n+1.\nI will explai
n 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 arbitrary height.\nTo show the ideas I may present quick proofs\, at th
e prime 2\, of the facts that K(ku) is height 2 and K(tmf) is height 3.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomer Schlank (Hebrew University)
DTSTART:20210222T213000Z
DTEND:20210222T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/24
DESCRIPTION:Title: Cyclotomic Galois extensions in the chromatic homotopy\nby Tome
r Schlank (Hebrew University) as part of MIT topology seminar\n\n\nAbstrac
t\nThe chromatic approach to stable homotopy theory is 'divide and conquer
'. That is\, questions about spectra are studies through various localizat
ions that isolate pure height phenomena and then are put back together. Fo
r each height n\, there are two main candidates for pure height localizati
on. The first is the generally more accessible K(n)-localization and the s
econd is the closely related T(n)-localization. It is an open problem whet
her the two families of localizations coincide.\n\nOne of the main reasons
that the K(n)-local category is more amenable to computations is the exis
tence of well understood Galois extensions of the K(n)-local sphere.\n\nIn
the talk\, I will present a generalization\, based on ambidexterity\, of
the classical theory of cyclotomic extensions\, suitable for producing non
-trivial Galois extensions in the T(n)-local and K(n)-local context. This
construction gives a new family of Galois extensions of the T(n)-local sph
ere 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 appli
cations\, including the study of the T(n)-local Picard group\, a chromatic
version 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://stable.researchseminars.org/talk/MITTop/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Achim Krause (University of Münster)
DTSTART:20210301T213000Z
DTEND:20210301T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/25
DESCRIPTION:Title: Title to be announced\nby Achim Krause (University of Münster)
as part of MIT topology seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Najib Idrissi (IMJ-PRG)
DTSTART:20210315T203000Z
DTEND:20210315T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/26
DESCRIPTION:Title: Configuration spaces of surfaces\nby Najib Idrissi (IMJ-PRG) as
part of MIT topology seminar\n\n\nAbstract\nFramed configuration spaces o
f a surface form a right module over the framed little disks operad. This
rich algebraic structure has important consequences\, for example for the
computations of manifold calculus or factorization homology. Determining t
he homotopy type of this operadic right module remains however a difficult
task. In this talk\, I will explain how to compute the rational homotopy
type for oriented compact surfaces. The end result is a finite-dimensional
purely combinatorial model. The proof involves several ingredients: Konts
evich’s formality\, Tamarkin’s formality\, and the cyclic formality of
the framed little disks operad. (Joint work with Ricardo Campos and Thoma
s Willwacher.)\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Wilson (Harvard University)
DTSTART:20210329T203000Z
DTEND:20210329T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/27
DESCRIPTION:Title: Variations on the theme of Lichtenbaum-Quillen\nby Dylan Wilson
(Harvard University) as part of MIT topology seminar\n\n\nAbstract\nIn re
cent work with Jeremy Hahn\, we established a higher chromatic version of
the Lichtenbaum-Quillen conjecture for truncated Brown-Peterson spectra. T
his talk will explore some questions raised by the proof\, and indicate so
me current and future lines of investigation. Some of what we will discuss
is also joint with Akhil Mathew.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nir Gadish (MIT)
DTSTART:20210405T203000Z
DTEND:20210405T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/28
DESCRIPTION:Title: Möbius inversion in hömotopy theory\nby Nir Gadish (MIT) as p
art of MIT topology seminar\n\n\nAbstract\nMöbius inversion is classicall
y a procedure in number theory that inverts summation of functions over th
e divisors of an integer. A similar construction is possible for every loc
ally finite poset\, and is governed by a so called Möbius function encodi
ng the combinatorics. In 1936 Hall observed that the values of the Möbius
function are Euler characteristics of intervals in the poset\, suggesting
a homotopy theoretic context for the inversion. In this talk we will disc
uss a functorial 'space-level' realization of Möbius inversion for diagra
ms taking values in a pointed cocomplete infinity-category. The role of th
e Möbius function will be played by hömotopy types whose reduced Euler c
haracteristics are the classical values\, and inversion will hold up to ex
tensions (think inclusion-exclusion but with the alternating signs replace
d by even/odd spheres).\n\nThis provides a uniform perspective to many con
structions in topology and algebra. Notable examples that I hope to mentio
n include handle decompositions\, Koszul resolutions\, and filtrations of
configuration spaces.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhulin Li (MIT)
DTSTART:20210412T203000Z
DTEND:20210412T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/29
DESCRIPTION:Title: Unstable modules with only the top k Steenrod operations\nby Zh
ulin Li (MIT) as part of MIT topology seminar\n\n\nAbstract\nIn this talk\
, I will introduce unstable modules with only the top k Steenrod operation
s at the prime 2. I'll show that they have projective dimension at most k.
Then I'll establish forgetful functors\, suspension functors\, loop funct
ors and Frobenius functors between such modules. The forgetful functors in
duce an inverse system of Ext groups\, and the inverse system stabilizes w
hen the covariant module is bounded above. In addition\, I will talk about
a generalization of the Lambda algebra which computes the Ext group from
such modules to suspensions of the base field.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Senger (MIT)
DTSTART:20210426T203000Z
DTEND:20210426T213000Z
DTSTAMP:20260404T094119Z
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 that the odd-primary Brown-Peterson spectrum does not admit the stru
cture of 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 a
t the prime 2.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Haine (MIT)
DTSTART:20210503T203000Z
DTEND:20210503T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/31
DESCRIPTION:Title: On the homotopy theory of stratified spaces\nby Peter Haine (MI
T) as part of MIT topology seminar\n\n\nAbstract\nA natural question arise
s when working with intersection cohomology and other stratified invariant
s of singular manifolds: what is the correct stable homotopy theory for th
ese invariants to live in? But before answering that question one first ha
s to identify the correct unstable homotopy theory of stratified spaces. T
he exit-path category construction of MacPherson\, Treumann\, and Lurie pr
ovides functor from suitably nice stratified topological spaces to “abst
ract stratified homotopy types” — ∞-categories with a conservative f
unctor to a poset. Work of Ayala–Francis–Rozenblyum even shows that th
eir conically smooth stratified topological spaces embed into the ∞-cate
gory of abstract stratified homotopy types. In this talk\, we explain some
of our work which goes further and produces an equivalence between the ho
motopy theory of all stratified topological spaces and these abstract stra
tified homotopy types.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Foling Zou (University of Michigan)
DTSTART:20210510T203000Z
DTEND:20210510T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/32
DESCRIPTION:Title: Nonabelian Poincare duality theorem and equivariant factorization h
omology of Thom spectra\nby Foling Zou (University of Michigan) as par
t of MIT topology seminar\n\n\nAbstract\nThe factorization homology are in
variants of n-dimensional manifolds with some fixed tangential structures
that take coefficients in suitable $\\mathbb{E}_n$-algebras. I will give a
definition for the equivariant factorization homology of a framed manifol
d for a finite group G via a monadic bar construction following Miller-Kup
ers. I will also talk about the unital variant of symmetric sequences that
is underneath this construction. Then I will talk about the equivariant n
onabelian Poincare duality theorem in this case and the equivariant factor
ization homology on equivariant spheres for certain Thom spectra. This is
joint with Asaf Horev\, Inbar Klang\, Peter May and Ruoqi Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elden Elmanto (Harvard University)
DTSTART:20210517T203000Z
DTEND:20210517T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/33
DESCRIPTION:Title: Trace methods for algebraic stacks.\nby Elden Elmanto (Harvard
University) as part of MIT topology seminar\n\n\nAbstract\nWe extend the D
undas-Goodwillie-McCarthy theorem concerning the fiber of the cyclotomic t
race map from K theory to topological cyclic homology\, to the context of
stable categories. Our main tool is Bondarko's theory of weight structures
. Applications include a new proof of cdh-descent for homotopy K-theory of
stacks (Hoyois-Krishna) and new cases of Blanc's lattice conjecture in no
ncommutative Hodge theory (ala Katzarkov-Kontsevich-Pantev). Time permitti
ng\, I will speak about vistas\, including the (equivariant) K-theory of t
he equivariant sphere and p-adic Hodge theory for stacks.\n\nThis is all j
oint work with Vova Sosnilo and partly based on https://arxiv.org/abs/2010
.09155\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke)
DTSTART:20210322T203000Z
DTEND:20210322T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/34
DESCRIPTION:Title: An excess intersection formula\nby Kirsten Wickelgren (Duke) as
part of MIT topology seminar\n\n\nAbstract\nOne expects the intersection
of a d and n-d dimensional subscheme or submanifold of an n-dimensional on
e to be 0 dimensional. When this is not the case\, such intersections are
often called excess intersections\, and arise when considering questions s
uch as 'How many conics are tangent to 5 conics in the plane?' We consider
cohomology 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 g
iving arithmetic refinements of counts classically valid only over algebra
ically closed fields. This is joint work with Tom Bachmann.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guozhen Wang (Shanghai Center for Mathematical Sciences)
DTSTART:20210705T140000Z
DTEND:20210705T150000Z
DTSTAMP:20260404T094119Z
UID:MITTop/35
DESCRIPTION:Title: Topological cyclic homology of local fields\nby Guozhen Wang (S
hanghai Center for Mathematical Sciences) as part of MIT topology seminar\
n\n\nAbstract\nWe introduce a new method for computing topological cyclic
homology of locally complete intersections over p-adic intergers\, by usin
g relative hochschild homology and resolving the base ring spectrum with a
n Adams reslolution. Using the Nygaard filtration on the E1-term\, we can
construct algebraic Tate and algebraic homotopy fixed points spectral sequ
ences\, which are algebraic and catpture lots of informations in the Tate
and homotopy fixed points spectral sequences computing TP and TC^{-1}. Usi
ng this method\, we can give a uniform way of computing topological cyclic
homology of local fields of mixed characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Land (University of Copenhagen)
DTSTART:20210712T140000Z
DTEND:20210712T150000Z
DTSTAMP:20260404T094119Z
UID:MITTop/36
DESCRIPTION:Title: Grothendieck—Witt theory of Dedekind rings and the stable cohomol
ogy of orthogonal and symplectic groups over Z\nby Markus Land (Univer
sity of Copenhagen) as part of MIT topology seminar\n\n\nAbstract\nI will
first give a brief overview of how one can understand classical Grothendie
ck—Witt theories of rings in terms of K-theoretic and L-theoretic pieces
. Using this\, I will explain how to determine various Grothendieck—Witt
theories\, in particular of Dedekind rings. As further application of the
se results\, I will then give a calculation of the stable cohomology of or
thogonal and symplectic groups over the integers focussing on the mod 2 co
homology.\n\n This is all based on joint work with Calmès\, Dotto\
, Harpaz\, Hebestreit\, Moi\, Nardin\, Nikolaus\, and Steimle\, and Hebest
reit and Nikolaus.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shachar Carmeli (Weizmann Institute of Science)
DTSTART:20210719T140000Z
DTEND:20210719T150000Z
DTSTAMP:20260404T094119Z
UID:MITTop/37
DESCRIPTION:Title: Higher semiadditivity and the K(1)-local sphere\nby Shachar Car
meli (Weizmann Institute of Science) as part of MIT topology seminar\n\n\n
Abstract\nHigher semiadditivity is a property of an infinity-category that
allows\, in particular\, for the summation of families of morphisms betwe
en objects parametrized by pi-finite spaces.\n\nHopkins and Lurie showed t
hat the K(n)-localizations of the infinity category of spectra are higher
semiadditive. Consequently\, by a work of Harpaz\, the mapping objects in
these infinity-categories admit the rich structure of higher commutative m
onoids.\nWhile many abstract properties of these higher commutative monoid
s are known\, 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 Al
len Yuan\, which aims to completely determine this higher commutative mono
id structure of the K(1)-local sphere. Specifically\, I will show how to u
se higher semiadditive versions of algebraic K-theory and Grothendieck-Wit
t theory 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 class
es in its homotopy groups as semiadditive cardinalities of pi-finite space
s\, and to compute explicitly certain power operations that arise from the
higher semiadditivity.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Yanovski (Max Planck Institute)
DTSTART:20210823T140000Z
DTEND:20210823T150000Z
DTSTAMP:20260404T094119Z
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 clas
sical discrete Fourier transform can be thought of as an isomorphism of ri
ngs between 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 analogous result in the chromatic world\, where the field of complex nu
mbers is replaced by the Lubin-Tate spectrum E_n\, the finite abelian grou
p A is replaced by a suitably finite p-power torsion Z-module spectrum\, a
nd the Pontryagin dual is modified by an n-fold suspension. From this\, th
ey deduce a number of structural properties of the infinity-category of K(
n)-local spectra\, such as affineness and Eilenberg-Moore type formulas fo
r pi-finite spaces. In this talk\, I will present a joint work with Barthe
l\, Carmeli\, and Sclank\, in which we develop the notion of a `higher Dis
crete Fourier transform' for general higher semiadditive infinity-categori
es. This allows us\, among other things\, to extend the above results of H
opkins and Lurie to the T(n)-local setting. Furthermore\, we study the int
eraction of Fourier transforms with categorification suggesting a close re
lationship to chromatic redshift phenomena. Finally\, by replacing Pontrya
gin duality with Brown-Comenetz duality\, we can contemplate the notion of
Fourier transform for more general pi-finite spectra than Z-modules\, lea
ding to questions intimately related to the behavior of the `discrepancy
spectrum'.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joana Cirici (Universitat de Barcelona)
DTSTART:20211108T213000Z
DTEND:20211108T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/39
DESCRIPTION:Title: Title to be announced.\nby Joana Cirici (Universitat de Barcelo
na) as part of MIT topology seminar\n\n\nAbstract\nAbstract to be shared.\
n
LOCATION:https://stable.researchseminars.org/talk/MITTop/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arpon Raksit (MIT)
DTSTART:20211115T213000Z
DTEND:20211115T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/40
DESCRIPTION:Title: Canonical lifts and spectral algebraic geometry\nby Arpon Raksi
t (MIT) as part of MIT topology seminar\n\n\nAbstract\nLet X be an ellipti
c curve over a perfect field k of positive characteristic. Serre–Tate st
udied the deformation theory of such X\, and one of their discoveries was
that when X is ordinary\, it admits a canonical lifting to the ring of Wit
t vectors W(k) (with some special features). In this talk\, I'll discuss a
connection between this phenomenon and properties of the moduli of ellipt
ic curves in spectral algebraic geometry introduced by Lurie.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hana Kong (IAS)
DTSTART:20211129T213000Z
DTEND:20211129T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/41
DESCRIPTION:Title: The homotopy of motivic image-of-j spectrum\nby Hana Kong (IAS)
as part of MIT topology seminar\n\nLecture held in Room: 2-131 in the MIT
Simons Building.\n\nAbstract\nBachmann–Hopkins defines the motivic 'ima
ge-of-j' spectrum over base fields with characteristic not 2. In this talk
\, I will talk about the effective slice computation of this spectrum over
the real numbers. Analogous to the classical story\, the result captures
a regular pattern that appears in the R-motivic stable stems. This is join
t work with Eva Belmont and Dan Isaksen.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Wilson (Harvard)
DTSTART:20211206T213000Z
DTEND:20211206T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/42
DESCRIPTION:Title: Title to be announced.\nby Dylan Wilson (Harvard) as part of MI
T topology seminar\n\nLecture held in Room: 2-131 in the MIT Simons Buildi
ng.\n\nAbstract\nabstract to be shared soon.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elden Elmanto (Harvard University)
DTSTART:20211122T213000Z
DTEND:20211122T223000Z
DTSTAMP:20260404T094119Z
UID:MITTop/43
DESCRIPTION:Title: Motivic cohomology reimagined\nby Elden Elmanto (Harvard Univer
sity) as part of MIT topology seminar\n\n\nAbstract\nBeilinson\, Macpherso
n and Schechtman asked us to imagine a world where topological K-theory wa
s first defined before singular cohomology. How would one invent the latte
r? This question has been influential to various approaches to motivic coh
omology of smooth varieties with its relationship to K-theory\, serving a
'design principle.' I will explain an extension of this idea to define a v
ersion of motivic cohomology of singular schemes. The engine behind it is
the Bhatt-Morrow-Scholze prismatic sheaves.\n\nThis is all joint work with
Tom Bachmann and Matthew Morrow.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Pstrągowski (Harvard University)
DTSTART:20220328T203000Z
DTEND:20220328T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/44
DESCRIPTION:Title: Quivers and the Adams Spectral Sequence\nby Piotr Pstrągowski
(Harvard University) as part of MIT topology seminar\n\nLecture held in Ro
om 2-131 in the Simons building.\n\nAbstract\nAssociated to each homology
theory we have an Adams spectral sequence computing stable homotopy classe
s of maps. Under flatness assumptions\, the E2-term can be identified with
cohomology of a certain Hopf algebroid\, giving the spectral sequence its
computational power. Unfortunately\, this identification fails in many im
portant examples\, such as integral homology or connective Morava K-theory
\, making these spectral sequences mysterious and hard to calculate with.
In this talk\, I will describe a novel method of identifying these E2-term
s in terms of cohomology in representations of certain quivers. This is ba
sed on joint work with Burklund.\n\nTo add this to your calendar\, the ics
file for this seminar is here:\nhttp://math.mit.edu/topology/topology_sem
inar.ics\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Sulyma (Brown University)
DTSTART:20220404T203000Z
DTEND:20220404T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/45
DESCRIPTION:Title: Floor Homotopy Theory\nby Yuri Sulyma (Brown University) as par
t of MIT topology seminar\n\nLecture held in Room 2-131 in the Simons Buil
ding.\n\nAbstract\nOne perspective on homotopy theory is that it is an enh
anced version of arithmetic which remembers combinatorics and symmetry. I
will demonstrate this philosophy concretely in the case of the floor and c
eiling functions from arithmetic\, by explaining several situations where
these appear: K-theory of truncated polynomial algebras\; Legendre's formu
la and its q-analogue\; hyper-representation-graded TR\; and equivariant h
omotopy theory. To understand how these examples are related\, I will show
how to construct a Tambara functor out of a prism\, and discuss a conject
ural theory of G-crystalline/G-de Rham cohomology generalizing q-crystalli
ne cohomology and the q-de Rham complex.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Araminta Amabel (MIT)
DTSTART:20220411T203000Z
DTEND:20220411T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/46
DESCRIPTION:Title: Title to be shared\nby Araminta Amabel (MIT) as part of MIT top
ology seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Burklund (MIT)
DTSTART:20220425T203000Z
DTEND:20220425T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/47
DESCRIPTION:Title: Title to be shared\nby Robert Burklund (MIT) as part of MIT top
ology seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yajit Jain (Brown University)
DTSTART:20220502T203000Z
DTEND:20220502T213000Z
DTSTAMP:20260404T094119Z
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\nAf
ter using smoothing theory to introduce a notion of exotic smooth structur
es on manifold bundles\, we will discuss an equivalent class of objects: s
mooth bundles of h-cobordisms with a topological trivialization. Using wor
k of Dwyer\, Weiss\, and Williams\, we will associate to such families an
invariant called the smooth structure class\, which is closely related to
the higher Franz-Reidemeister torsion of Igusa and Klein. We will illustra
te two proofs of a duality theorem for the smooth structure class. This th
eorem generalizes Milnor's duality theorem for Whitehead torsion. A conseq
uence of this result is the rigidity conjecture of Goette and Igusa\, whic
h states that\, after rationalizing\, stable exotic smoothings of manifold
bundles with closed even dimensional fibers do not exist.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Riggenbach (Northwestern University)
DTSTART:20220509T203000Z
DTEND:20220509T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/49
DESCRIPTION:Title: NTC of Perfectoid Rings\nby Noah Riggenbach (Northwestern Unive
rsity) as part of MIT topology seminar\n\nLecture held in Room: 2-131 in t
he MIT Simons Building.\n\nAbstract\nIn this talk I will discuss my recent
computation of the NTC groups of perfectoid rings which have a system of
pth power 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). T
his includes all perfect fields of positive characteristic\, for which the
se groups vanish in non-negative degrees. This class of rings also contain
s many mixed characteristic rings\, and perhaps surprisingly while the eve
n nonnegative groups will still vanish\, the odd groups will not.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART:20220919T190000Z
DTEND:20220919T200000Z
DTSTAMP:20260404T094119Z
UID:MITTop/50
DESCRIPTION:Title: Syntomic complexes of regular rings\nby Akhil Mathew (Universit
y of Chicago) as part of MIT topology seminar\n\nLecture held in Room 2-13
1.\n\nAbstract\nSyntomic complexes are a form of p-adic motivic cohomology
that filter p-adic \\’etale K-theory (or topological cyclic homology)\,
and which are defined in terms of prismatic cohomology. I will explain a
description of the syntomic complexes of p-torsionfree regular rings\, bas
ed on a mixed characteristic analog of the Cartier isomorphism\, closely r
elated to the Segal conjecture for THH. (Joint with Bhargav Bhatt.)\n\nSpe
cial Seminar Time at 3pm!\n\nThe seminar will meet at 4:30 on Mondays in 2
-131 unless otherwise noted.\n\nClick here to add this seminar to your goo
gle calendar. If you use a different calendar program\, the ics file for t
his seminar is here:\nhttp://math.mit.edu/topology/topology_seminar.ics\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arpon Raksit (MIT)
DTSTART:20220926T203000Z
DTEND:20220926T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/51
DESCRIPTION:Title: The Even Filtration\nby Arpon Raksit (MIT) as part of MIT topol
ogy seminar\n\nLecture held in Room 2 - 131.\n\nAbstract\nThis talk will b
e about joint work with Jeremy Hahn and Dylan Wilson in which we define a
filtration on an arbitrary commutative ring spectrum that we call the "eve
n filtration". I'll introduce the definition\, the one method we've come u
p with for analyzing it\, and its relation to other filtrations of interes
t\, in particular motivic filtrations on topological Hochschild homology.\
n
LOCATION:https://stable.researchseminars.org/talk/MITTop/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Kuhn (University of Virginia)
DTSTART:20221003T203000Z
DTEND:20221003T213000Z
DTSTAMP:20260404T094119Z
UID:MITTop/52
DESCRIPTION:Title: Chromatic Fixed Point Theory\nby Nick Kuhn (University of Virgi
nia) 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 fini
te p-group G on a finite G-CW complex X is one of the oldest topics in alg
ebraic topology. In the late 1930's\, P. A. Smith proved that if X is mod
p acyclic\, then so is XG\, its subspace of fixed points. A related theore
m of Ed Floyd from the early 1950's says that the dimension of the mod p h
omology of X will bound the dimension of the mod p homology of XG.\n\n\\sm
allskip\n\nThe study of the Balmer spectrum of the homotopy category of G-
spectra has lead to the problem of identifying "chromatic" variants of Smi
th's theorem\, with mod p homology replaced by the Morava K-theories (at t
he prime p). One such chromatic Smith theorem is proved by Barthel et.al.:
if G is a cyclic p-group and X is K(n) acyclic\, then XG is K(n−1) acyc
lic (and this answers questions like this for all abelian p-groups).\n\n\\
smallskip\n\nIn work with Chris Lloyd\, we have been able to show that a c
hromatic analogue of Floyd's theorem is true whenever a chromatic Smith th
eorem holds. For example\, if G is a cyclic p-group\, then the dimension o
ver 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 im
ply the stronger chromatic Floyd theorems uses the representation theory o
f the symmetric groups.\n\n\\smallskip\n\nThese chromatic Floyd theorems o
pen the door for many applications. We have been able to resolve open ques
tions involving the Balmer spectrum for the extraspecial 2-groups. In a di
fferent direction\, at the prime 2\, we can show quick collapsing of the A
HSS computing the Morava K-theory of some real Grassmanians: this is a non
-equivariant result.\n\n\\smallskip\n\nIn my talk\, I'll try to give an ov
erview of some of this.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Rivera (Purdue University)
DTSTART:20221017T140000Z
DTEND:20221017T150000Z
DTSTAMP:20260404T094119Z
UID:MITTop/53
DESCRIPTION:Title: Simplicial coalgebras under three different notions of weak equival
ence\nby Manuel Rivera (Purdue University) as part of MIT topology sem
inar\n\n\nAbstract\n\\noindent Motivated by constructing algebraic models
for homotopy types\, I will discuss three different homotopy theories on t
he category of simplicial cocommutative coalgebras corresponding to the fo
llowing notions of weak equivalence:\n\n\\vspace{2ex}\n\n\\begin{itemize}\
n\n\\item 1. maps of simplicial coalgebras which become quasi-isomorphisms
of differential graded (dg) coalgebras after applying the normalized chai
ns functor\n\n\\item 2. maps of simplicial coalgebras which become quasi-i
somorphisms of dg algebras after applying the normalized chains functor fo
llowed by the dg cobar construction\, and\n\n\\item 3. maps of simplicial
coalgebras which become quasi-isomorphisms of dg algebras after applying a
localized version of the dg cobar construction.\n\n\\end{itemize}\n\n\\vs
pace{2ex}\n\n\\noindent Notion (1) was used by Goerss to provide a fully-f
aithful model for spaces up to F-homology equivalence\, for a F an algebra
ically closed field. I will explain how (2)\, which is drawn from dg Koszu
l duality theory\, corresponds to a linearized version of the notion of ca
tegorical equivalence between simplicial sets as used in the theory of qua
si-categories. I will also explain how (3) leads to a fully-faithful model
for the homotopy theory of simplicial sets considered up to maps that ind
uce isomorphisms on fundamental groups and on the F-homology of the univer
sal covers\, 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 joint work with G. Raptis and also on work with F. Wierstra and M. Zei
nalian.\n
LOCATION:https://stable.researchseminars.org/talk/MITTop/53/
END:VEVENT
END:VCALENDAR