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BEGIN:VEVENT
SUMMARY:Robert Burklund (University of Copenhagen)
DTSTART:20230911T200000Z
DTEND:20230911T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/1
DESCRIPTION:Title: Beyond the telescope conjecture\nby Robert Burklun
d (University of Copenhagen) as part of MIT Algebraic Topology Seminar\n\n
Lecture held in 2-131.\n\nAbstract\nThere is a natural dichotomy between t
elescopic (T(n)-local) and chromatic (K(n)-local) homotopy theory. Telesco
pic homotopy theory is more closely tied to the stable homotopy groups of
spheres and through them to geometric questions\, but is generally computa
tionally intractable. Chromatic homotopy theory is more closely tied to ar
ithmetic geometry and powerful computational tools exist in this setting.
Ravenel’s telescope conjecture asserted that these two sides coincide. I
will present a family of counterexamples to this conjecture based on usin
g trace methods to analyze the algebraic K-theory of a family of K(n)-loca
l ring spectra beginning with the K(1)-local sphere. As a consequence of t
his we obtain a new lower bound on the average rank of the stable homotopy
groups of spheres. Time permitting\, I will then describe the galois grou
p of the T(n)-local sphere and how this informs our understanding of teles
copic homotopy theory. This talk is based on projects joint with Carmeli\,
Clausen\, Hahn\, Levy\, Schlank and Yanovski.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Antieau (Northwestern University)
DTSTART:20230918T203000Z
DTEND:20230918T220000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/2
DESCRIPTION:Title: Integral models for spaces\nby Ben Antieau (Northw
estern University) as part of MIT Algebraic Topology Seminar\n\nLecture he
ld in 2-131.\n\nAbstract\nGeneralizing and building on the work of Kriz\,
Ekedahl\, Goerss\, Lurie\, Mandell\, Mathew\, Mondal\, Quillen\, Sullivan\
, Toën and Yuan\, I will describe an integral cochain model for nilpotent
spacees of finite type. A binomial ring is a lambda-ring in which all Ada
ms operations act as the identity. A derived binomial ring is a derived Λ
-ring equipped with simultaneous trivializations of the commuting Adams op
erations. For example\, if X is a space\, then ZX\, the integral cochains
on X\, is naturally a derived binomial ring. The induced contravariant fun
ctor from spaces to derived binomial rings is fully faithful when restrict
ed to nilpotent spaces of finite type. This is related\, closely\, to rece
nt work of Horel and of Kubrak—Shuklin—Zakharov.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hana Jia Kong (Harvard University)
DTSTART:20230925T203000Z
DTEND:20230925T220000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/3
DESCRIPTION:Title: A deformation of Borel equivariant homotopy\nby Ha
na Jia Kong (Harvard University) as part of MIT Algebraic Topology Seminar
\n\nLecture held in 2-131.\n\nAbstract\nThe real motivic stable homotopy c
ategory has a close connection\nto the $C_2$-equivariant stable homotopy c
ategory. From a computational perspective\, the real motivic computation c
an be viewed\nas a simpler version which “removes the negative cone” i
n the $C_2$-\nequivariant stable homotopy groups. On the other hand\, by w
ork of\nBurklund–Hahn–Senger\, one can build the completed Artin–Tat
e real\nmotivic category from the completed $C_2$-equivariant category usi
ng\nthe deformation construction associated to the $C_2$-effective filtrat
ion.\nIn work with Gabriel Angelini-Knoll\, Mark Behrens\, and Eva Belmont
\,\nwe try to build an analog of this deformation story for a general fini
te\ngroup $G$. We give a new interpretation of the $C_2$-effective filtrat
ion\nin the Borel equivariant category which generalizes for $G$. Using th
is\nnew interpretation\, the deformation construction gives a deformation\
nof the Borel equivariant stable homotopy category for general finite\ngro
ups.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Berwick-Evans (University of Illinois Urbana-Champaign)
DTSTART:20231002T203000Z
DTEND:20231002T220000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/4
DESCRIPTION:Title: Supersymmetric field theories and elliptic cohomology<
/a>\nby Dan Berwick-Evans (University of Illinois Urbana-Champaign) as par
t of MIT Algebraic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\
nSince the mid 1980s\, there have been hints of a deep connection between
2-dimensional field theories and elliptic cohomology. This lead to Stolz a
nd Teichner's conjectured geometric model for the universal elliptic cohom
ology theory of topological modular forms (TMF) in which cocycles are 2-di
mensional supersymmetric field theories. Basic properties of these field t
heories lead to expected integrality and modularity properties\, but the a
bundant torsion in TMF has always been mysterious. In this talk\, I will d
escribe deformation invariants of 2-dimensional field theories that realiz
e some of the torsion in TMF.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Brazelton (Harvard University)
DTSTART:20231016T203000Z
DTEND:20231016T220000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/5
DESCRIPTION:by Thomas Brazelton (Harvard University) as part of MIT Algebr
aic Topology Seminar\n\nLecture held in 2-131.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Pstrągowski (Harvard University)
DTSTART:20231023T203000Z
DTEND:20231023T220000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/6
DESCRIPTION:Title: The even filtration and prismatic cohomology\nby P
iotr Pstrągowski (Harvard University) as part of MIT Algebraic Topology S
eminar\n\nLecture held in 2-131.\n\nAbstract\nThe even filtration\, introd
uced by Hahn-Raksit-Wilson\, is a canonical filtration attached to a commu
tative ring spectrum which measures its failure to be even. Despite its si
mple definition\, the even filtration recovers many arithmetically importa
nt constructions\, such as the Adams-Novikov filtration of the sphere or t
he Bhatt-Morrow-Scholze filtration on topological Hochschild homology\, sh
owing that they are all invariants of the commutative ring spectrum alone.
I will describe a linear variant of the even filtration which is naturall
y defined on associative rings and can be effectively calculated through r
esolutions of modules\, as well as joint work with Raksit on the resulting
extension of prismatic cohomology to the context of $E_2$-rings.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomer Schlank (Hebrew University of Jeruselam)
DTSTART:20231030T203000Z
DTEND:20231030T220000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/7
DESCRIPTION:Title: Higher Semi-additivity and Chromatically localized $K$
-theory\nby Tomer Schlank (Hebrew University of Jeruselam) as part of
MIT Algebraic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nWe s
hall consider the functor $L_{T(n)}K $ of chromatically localized algebrai
c $K$-theory. We shall discuss its interaction with pi-finite colimits. Th
is will lead to a possible alternative characterization of this functor as
well as results about it's interaction with cyclotomic hyper-descent. Thi
s is a key input to the proof of the telescope conjecture. This talk is ba
sed on joint works with Shay Ben-Moshe\, Shachar Carmeli\, and Lior Yanovs
ki\, as well as with Robert Burklund\, Jeremy Hahn\, and Ishan Levy.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20231106T213000Z
DTEND:20231106T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/8
DESCRIPTION:Title: The rational homotopy groups of the $K(n)$-local spher
e\nby Jared Weinstein (Boston University) as part of MIT Algebraic Top
ology Seminar\n\nLecture held in 2-131.\n\nAbstract\nWe compute the ration
al homotopy groups of the $K(n)$-local sphere for all heights $n$ and all
primes $p$\, verifying a prediction that goes back to Morava in the early
1970s. The key ingredients are (1) the Devinatz-Hopkins spectral sequence
(2) the isomorphism between the Lubin–Tate tower and the Drinfeld tower
at the level of perfectoid spaces (3) integral $p$-adic Hodge theory\, and
(4) an integral refinement of a theorem of Tate on the Galois cohomology
of nonarchimedean fields. This is joint work with Tobias Barthel\, Tomer S
chlank\, and Nathaniel Stapleton.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Westerland (University of Minnesota)
DTSTART:20231113T200000Z
DTEND:20231113T210000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/9
DESCRIPTION:Title: Moments of L-functions via the homology of braid group
s.\nby Craig Westerland (University of Minnesota) as part of MIT Algeb
raic Topology Seminar\n\nLecture held in The seminar will meet at 3:00 PM
in Harvard Science Center SC507 at Arithmetic Statistics seminar..\n\nAbst
ract\nIn 2005\, Conrey\, Farmer\, Keating\, Rubinstein\, and Snaith posed
a conjecture on the asymptotics of moments of quadratic L-functions. While
this conjecture originates as a question about number fields\, it has a m
ore geometric version when posed over function fields in positive characte
ristic. I’ll talk about how one can reinterpret the central object in th
is conjecture in terms of the action of the Galois group of a finite field
on the cohomology of braid groups with certain coefficients coming from t
he braid group’s interpretation as the hyperelliptic mapping class group
. We will see the “arithmetic factor” in this conjecture appear in the
part of this cohomology that is accessible through tools of homological s
tability. This is joint work with Jonas Bergström\, Adrian Diaconu\, and
Dan Petersen.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART:20231204T213000Z
DTEND:20231204T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/10
DESCRIPTION:by Akhil Mathew (University of Chicago) as part of MIT Algebra
ic Topology Seminar\n\nLecture held in 2-131.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Lesh (Union College)
DTSTART:20231127T213000Z
DTEND:20231127T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/11
DESCRIPTION:Title: Normalizer decompositions of p-local compact groups\nby Kathryn Lesh (Union College) as part of MIT Algebraic Topology Semi
nar\n\nLecture held in 2-131.\n\nAbstract\nI will talk about a 'normalizer
decomposition' for the classifying space of a p-local compact group. The
decomposition generalizes those of Dwyer for finite groups and of Libman f
or p-local finite groups and (separately) for compact Lie groups. I'll sho
w how the decomposition gives a homotopy pushout square for the exotic p-c
ompact groups of Aguade and Zabrodsky by building on the example of SU(p).
This is joint work with Belmont\, Castellana\, Grbic\, and Strumila.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Efimov (Steklov Mathematical Institute of Russian Academ
y of Sciences and National Research University Higher School of Economics)
DTSTART:20240129T213000Z
DTEND:20240129T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/12
DESCRIPTION:Title: Localizing motives and corepresentability of $TR$ and
$TC$\nby Alexander Efimov (Steklov Mathematical Institute of Russian
Academy of Sciences and National Research University Higher School of Econ
omics) as part of MIT Algebraic Topology Seminar\n\nLecture held in 2-131.
\n\nAbstract\nI will explain some of my recent results on the category of
localizing motives -- the target of the universal localizing invariant com
muting with filtered colimits. The main surprising result about this categ
ory is that it is rigid as a symmetric monoidal category (in the sense of
Gaitsgory and Rozenblyum).\n \n\nAs an application of the proof of rigidit
y\, we will deduce that the functors $TR$ (topological restriction) and $T
C$ (topological cyclic homology) are corepresentable in this category\, if
we restrict to connective $E_1-rings$.\n\nIf time permits\, I will explai
n how rigidity of $Mot^loc$ allows to construct refined versions of (topol
ogical) Hochschild homology and its variants\, which contain much more inf
ormation about the $E_1-algebra$ than the usual variants of $(T)HH$.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Belmont (Case Western Reserve University)
DTSTART:20240205T213000Z
DTEND:20240205T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/13
DESCRIPTION:Title: Computations with the modified Adams spectral sequenc
e\nby Eva Belmont (Case Western Reserve University) as part of MIT Alg
ebraic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nThe modifie
d Adams spectral sequence\, which computes the homotopy groups of a Borel-
equivariant spectrum\, is a combination of the homotopy fixed points spect
ral sequence and the nonequivariant Adams spectral sequence. One can also
use it to read off (completed) $\\mathbb{R}$-motivic homotopy groups\, via
a synthetic spectra construction. We will explain how to compute it using
examples coming from $ko_{C_2}$ and $kq$. This is joint work with Gabriel
Angelini-Knoll\, Mark Behrens\, and Hana Kong.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Angelini-Knoll (Sorbonne Paris Nord)
DTSTART:20240304T213000Z
DTEND:20240304T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/14
DESCRIPTION:Title: Syntomic cohomology of real topological $K$-theory\nby Gabriel Angelini-Knoll (Sorbonne Paris Nord) as part of MIT Algebrai
c Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nWork of Hahn-Rak
sit-Wilson extended the Bhatt-Morrow-Scholze filtration on topological cyc
lic homology and topological periodic cyclic homology to sufficiently nice
ring spectra. This allows one to define syntomic cohomology and prismatic
cohomology at this level of generality. One example of such a nice ring s
pectrum is real topological $K$-theory. In joint work with Christian Auson
i and John Rognes\, we compute the syntomic cohomology of real topological
$K$-theory modulo $(2\,η\,v_1)$. This computation produces a new example
of pure redshift and arithmetic duality. As an application\, we compute t
he algebraic $K$-theory of real topological $K$-theory modulo $(2\,η\,v_1
)$ and show that it satisfies a higher chromatic complexity version of the
Lichtenbaum-Quillen conjecture.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen McKean (Harvard University)
DTSTART:20240311T203000Z
DTEND:20240311T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/15
DESCRIPTION:Title: Motivic Euler characteristics and power structures\nby Stephen McKean (Harvard University) as part of MIT Algebraic Topolog
y Seminar\n\nLecture held in 2-131.\n\nAbstract\nThere is a quadratic form
-valued version of the compactly supported Euler characteristic coming fro
m motivic homotopy. A feature of this Euler characteristic is that it desc
ends to a ring homomorphism out of the Grothendieck ring of varieties. In
characteristic 0\, this Euler characteristic was constructed by Röndigs a
nd later Arcila-Maya—Bethea—Opie—Wickelgren—Zakharevich\, who used
Bittner’s blow up presentation of $K_0(Var)$. In characteristic not 2\,
Azouri gave a characterization in terms of the six functor formalism. I w
ill discuss a hybrid approach using a sort of universal property of $K_0(V
ar)$. I will then discuss power structures on $K_0(Var)$ and the Grothendi
eck—Witt ring of quadratic forms\, and conclude with a conjecture relati
ng these two power structures. This is joint work in progress with Dori Be
jleri\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Pstrągowski (Kyoto University)
DTSTART:20250117T213000Z
DTEND:20250117T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/16
DESCRIPTION:Title: The monochromatic Hahn-Wilson conjecture\nby Piot
r Pstrągowski (Kyoto University) as part of MIT Algebraic Topology Semina
r\n\nLecture held in 2-449.\n\nAbstract\nIn 1999\, Mark Mahowald and Charl
es Rezk introduced a class of spectra which are particularly amenable to u
nderstanding using the classical Adams spectral sequence\, called fp-spect
ra. As first described by Rognes\, these play a pivotal role in generalizi
ng Quillen-Lichtenbaum conjectures to the setting of ring spectra.\n\nThe
Quillen-Lichtenbaum conjectures were proven for truncated Brown-Peterson s
pectra by Dylan Wilson and Jeremy Hahn in 2021\, who in this way discovere
d the first highly non-obvious example of an fp-spectrum in the form of al
gebraic $K$-theory. This led them to ask about a general structure result
for fp-spectra\, and to conjecture that they can all be built out of parti
cularly simple ones.\n\nI will talk about recent joint work with David Lee
where we prove a monochromatic analogue of the Hahn-Wilson conjecture\, a
nd deduce the original conjecture at height one.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Søren Galatius (Columbia University)
DTSTART:20250203T213000Z
DTEND:20250203T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/17
DESCRIPTION:Title: Hopf algebra spectral sequences related to $\\textit{
K}(\\mathbb{Z}$) and the Grothendieck–Teichmüller group\nby Søren
Galatius (Columbia University) as part of MIT Algebraic Topology Seminar\n
\nLecture held in 2-131.\n\nAbstract\nThe general linear group of the inte
gers acts on the symmetric space $GL_n(\\mathbb{R})/O(n)$\, and the orbit
space $X_n$ can be regarded as a “moduli space of real tori”. The comp
actly supported cohomology of these spaces forms the $E_1$ page of a spect
ral sequence converging to the cohomology of $BK(\\mathbb{Z})$\, the onefo
ld delooping of the algebraic $K$-theory space. I will sketch how to const
ruct a Hopf algebra structure on this spectral sequence\, and how it maps
to another spectral sequence of Hopf algebras\, a version of the Connes–
Kreimer Hopf algebra. In recent joint work with Brown\, Chan\, and Payne (
2405.11528)\, we use this map of Hopf algebras to deduce lower bounds for
the compactly supported cohomology of $X_n$ and of $A_n$\, the moduli spac
e of principally polarized abelian varieties.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Knudsen (Northeastern University)
DTSTART:20250224T213000Z
DTEND:20250224T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/18
DESCRIPTION:Title: Probabilistic invariants of finite groups\nby Ben
Knudsen (Northeastern University) as part of MIT Algebraic Topology Semin
ar\n\nLecture held in 2-131.\n\nAbstract\nWe continue the study of the pro
babilistic versions of the Lusternik–Schnirelmann category and topologic
al complexity introduced in joint work with Weinberger and independently b
y Dranishnikov–Jauhari. In the aspherical context\, where these invarian
ts are group invariants\, there is a universal upper bound in the finite c
ase. We discuss progress toward calculating the exact value\, which is equ
ivalent to an interesting problem in equivariant homotopy theory. This tal
k is based on joint work with Shmuel Weinberger.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirai Ikebuchi (Kyoto University)
DTSTART:20250303T213000Z
DTEND:20250303T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/19
DESCRIPTION:Title: Quillen cohomology of small cartesian closed categori
es\nby Mirai Ikebuchi (Kyoto University) as part of MIT Algebraic Topo
logy Seminar\n\nLecture held in 2-131.\n\nAbstract\nCohomology of Lawvere
theories — small categories with finite products\, also called algebraic
theories — is studied by Jibladze and Pirashvili. They considered three
types of definitions\, Quillen\, Baues-Wirsching\, and Ext cohomologies\,
and showed that their equivalences. In this talk\, we extend their work t
o small cartesian closed categories. Also\, we will briefly see its applic
ation to logic and theoretical computer science. As Lawvere theories are c
ategorical formulation of universal algebra\, there is a famous correspond
ence between cartesian closed categories and equational theories on simply
typed lambda calculus. So\, cohomology of cartesian closed categories is
an invariant of such equational theories.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cary Malkiewich (Binghamton University)
DTSTART:20250331T203000Z
DTEND:20250331T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/20
DESCRIPTION:Title: Higher scissors congruence\nby Cary Malkiewich (B
inghamton University) as part of MIT Algebraic Topology Seminar\n\nLecture
held in 2-131.\n\nAbstract\nScissors congruence is the study of polytopes
\, up to the relation of cutting into finitely many pieces and rearranging
the pieces. In the 2010s\, Zakharevich defined a "higher" version of scis
sors congruence\, where we don't just ask whether two polytopes are scisso
rs congruent\, but also how many scissors congruences there are from one p
olytope to another.\n\nZakharevich's definition is a form of algebraic K-t
heory\, which is famously difficult to compute\, but I will discuss a surp
rising result that makes the computation of the higher K-groups possible\,
at least for low-dimensional geometries. In particular\, this gives the h
omology of the group of interval exchange transformations\, and a new proo
f of Szymik and Wahl's theorem that Thompson's group V is acyclic. Much of
this talk is based on joint work with Anna-Marie Bohmann\, Teena Gerhardt
\, Mona Merling\, and Inna Zakharevich\, and also with Alexander Kupers\,
Ezekiel Lemann\, Jeremy Miller\, and Robin Sroka.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J.D. Quigley (University of Virginia)
DTSTART:20250421T203000Z
DTEND:20250421T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/21
DESCRIPTION:by J.D. Quigley (University of Virginia) as part of MIT Algebr
aic Topology Seminar\n\nLecture held in 2-131.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Senger (Harvard University)
DTSTART:20250428T203000Z
DTEND:20250428T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/22
DESCRIPTION:by Andy Senger (Harvard University) as part of MIT Algebraic T
opology Seminar\n\nLecture held in 2-131.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Spitz (University of Virginia)
DTSTART:20250210T213000Z
DTEND:20250210T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/23
DESCRIPTION:Title: The Tambara Affine Line\nby Ben Spitz (University
of Virginia) as part of MIT Algebraic Topology Seminar\n\nLecture held in
2-131.\n\nAbstract\nIn equivariant stable homotopy theory\, objects calle
d "Tambara functors" play the role of commutative rings. Tambara functors
are abstract algebraic objects: they consist of sets with certain operatio
ns satisfying certain axioms\; however\, the theory of Tambara functors is
much less developed than the theory of commutative rings\, in part becaus
e it is not clear exactly how to define the "Tambara analogs" of many clas
sical notions. Nonetheless\, we expect that Tambara functors admit a theor
y of commutative algebra and algebraic geometry\, akin to the story for or
dinary commutative rings. In this talk\, I will discuss recent progress in
developing such a theory for Tambara functors – in particular\, we prov
e a version of the going-up theorem\, which allows for the first computati
on of the "affine line" in Tambara algebraic geometry. This is joint work
with David Chan\, David Mehrle\, J.D. Quigley\, and Danika Van Niel.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART:20250505T203000Z
DTEND:20250505T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/24
DESCRIPTION:Title: A Hopf algebra in the cohomology of moduli of abelian
varieties\nby Melody Chan (Brown University) as part of MIT Algebraic
Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nI will discuss as
pects of joint work with Brown\, Galatius\, and Payne. In particular\, we
identify a Hopf algebraic structure in the weight 0 cohomology with compac
t supports of the moduli space of abelian varieties\, and we deduce expone
ntial growth results as a corollary. A key role is played by the moduli sp
ace of tropical abelian varieties\, which is stratified by locally symmetr
ic spaces $GL_n(Z)\\GL_n(R)/O(n)$. I will try to emphasize aspects of this
work not discussed in Galatius' talk in this seminar.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dev Sinha (University of Oregon)
DTSTART:20250310T203000Z
DTEND:20250310T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/25
DESCRIPTION:Title: From Milnor invariants to $E$-infinity cochain struct
ures\nby Dev Sinha (University of Oregon) as part of MIT Algebraic Top
ology Seminar\n\nLecture held in 2-131.\n\nAbstract\nWe share current work
which goes back and forth between geometric and algebraic topology. We st
art with generalization of Milnor invariants of links\, which works beyond
where their indeterminacy limits them and extends to links any three-mani
fold. This generalization arises from analysis of the classical bar constr
uction. (So we are making progress by connecting two pieces of mathematics
developed in Fine Hall in the 1950’s.) These ideas also lead to new alg
orithms to produce all polynomial functions on presented groups. We then s
hare recent work relating cup product to intersection product on geometric
cochains through vector field flows. This leads to a conjectural new appr
oach to $E$-infinity structure on cochains by “resolving partial-defined
ness” rather than resolving non-commutativity. What unites these project
s is a goal of producing homotopy invariants through a combination of tool
s including geometric cochains\, configuration spaces and bar construction
s.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rok Gregoric / David Lee (John Hopkins University / MIT)
DTSTART:20250414T203000Z
DTEND:20250414T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/26
DESCRIPTION:by Rok Gregoric / David Lee (John Hopkins University / MIT) as
part of MIT Algebraic Topology Seminar\n\nLecture held in 2-131.\n\nAbstr
act\nRok Gregoric (Johns Hopkins University) at 3 PM in 2-449\n\nDavid Lee
(MIT) at 4:30 PM in 2-131\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ishan Levy (University of Copenhagen)
DTSTART:20250512T203000Z
DTEND:20250512T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/27
DESCRIPTION:Title: The spectral Sullivan conjecture\nby Ishan Levy (
University of Copenhagen) as part of MIT Algebraic Topology Seminar\n\nLec
ture held in 2-131.\n\nAbstract\nThe Sullivan conjecture\, proven by Mille
r in 1984\, says that the space of pointed maps from $BC_p$ to a finite di
mensional CW-complex is contractible. I will explain a generalization of t
his\, where $BC_p$ can be replaced with any connected $p$-nilpotent infin
ite loop space. I will also describe some consequences and questions surro
unding this result.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Muñoz-Echániz (MIT)
DTSTART:20250915T203000Z
DTEND:20250915T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/28
DESCRIPTION:Title: A Weiss–Williams theorem for embedding spaces and a
n application to diffeomorphisms of solid tori\nby Samuel Muñoz-Echá
niz (MIT) as part of MIT Algebraic Topology Seminar\n\nLecture held in 2-1
31.\n\nAbstract\nThere is a programme\, largely developed by Weiss and Wil
liams\, that aims to understand the homotopy type of the diffeomorphism gr
oup of a compact\, high-dimensional manifold $M$ in terms of Waldhausen's
algebraic $K$-theory of $M$. In this talk\, I will give a brief overview o
f this programme and present an analogue for spaces of embeddings (of comp
act manifolds $P$ into $M$\, say). The main difference with the original p
rogramme is that the algebraic $K$-theory of $M$ is replaced by the *relat
ive* algebraic $K$-theory of the pair ($M\, M$ - $P$)\, which\, in many ca
ses\, coincides with the relative topological cyclic homology of such pai
r — a far more computable invariant. \n\nAs an application\, I will repo
rt on ongoing joint work with João Lobo Fernandes computing rational homo
topy groups of the diffeomorphism group of solid tori $S^1 \\times D^n\, n
> 4$. This follows a strategy of Bustamante–Randal-Williams and extends
computations of Budney–Gabai and Watanabe in high-dimensions.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Behrens (University of Notre Dame)
DTSTART:20250922T203000Z
DTEND:20250922T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/29
DESCRIPTION:Title: A $C_3$-equivariant Snaith construction\nby Mark
Behrens (University of Notre Dame) as part of MIT Algebraic Topology Semin
ar\n\nLecture held in 2-131.\n\nAbstract\nSnaith showed that the periodic
complex cobordism spectrum MUP can be obtained by localizing the suspensio
n spectrum of BU with respect to the generator of $\\pi_2$. Chatham\, Hah
n\, and Yuan proved analogs of this theorem where BU is replaced by a gene
ral Wilson space. We consider the localization of the equivariant suspens
ion spectrum of a $C_3$-equivariant Wilson space. I will describe work in
progress which compares this spectrum to the spectrum $BP_mu3$ constructe
d by Hu\, Kriz\, Somberg\, and Zou. We will revisit their construction\,
and flesh out some details. This represents joint work with Gabe Angelini
-Knoll\, Max Johnson\, and Hana Jia Kong.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rok Gregoric (Johns Hopkins University)
DTSTART:20250929T203000Z
DTEND:20250929T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/30
DESCRIPTION:Title: Even periodization of spectral stacks\nby Rok Gre
goric (Johns Hopkins University) as part of MIT Algebraic Topology Seminar
\n\nLecture held in 2-131.\n\nAbstract\nIn this talk\, we will introduce a
nd discuss even periodization: an operation which approximates a spectral
stack as closely as possible by affines corresponding to even periodic rin
g spectra. We will discuss how this recovers and geometrizes the even filt
ration of Hahn-Raksit-Wilson\, and how it gives rise to canonical spectral
enhancements of versions of the prismatization stacks of Bhatt-Lurie and
Drinfeld\, extending the approach to prismatic cohomology via topological
Hochschild homology of Bhatt-Morrow-Scholze.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhouli Xu (University of California\, Los Angeles)
DTSTART:20251006T203000Z
DTEND:20251006T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/31
DESCRIPTION:Title: Proof of the existence of $\\theta_6$\nby Zhouli
Xu (University of California\, Los Angeles) as part of MIT Algebraic Topol
ogy Seminar\n\nLecture held in 2-131.\n\nAbstract\nThe Kervaire invariant
problem asks in which dimensions there exists a stably framed manifold of
Kervaire invariant one. Hill-Hopkins-Ravenel resolved this problem in all
but one dimension: 126.\n\n\nIn this talk\, I will present an overview of
the proof that $h_6^2$ survives in the Adams spectral sequence\, thereby r
esolving the final open case of the Kervaire invariant problem. I will dis
cuss new techniques involved\, some of which are inspired by motivic homot
opy theory. This is joint work with Weinan Lin and Guozhen Wang.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20251020T203000Z
DTEND:20251020T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/32
DESCRIPTION:Title: On the splitting conjecture of Hopkins\nby Jared
Weinstein (Boston University) as part of MIT Algebraic Topology Seminar\n\
nLecture held in 2-131.\n\nAbstract\nHopkins' splitting conjecture predict
s the structure of a double localization $L_{K(t)} L_{K(h)} S$ of the sphe
re spectrum\, where $K(h)$ is Morava $K$-theory at a prime $p$ and $0 < t
< h$. \nPerfectoid techniques give powerful evidence for the conjecture w
hile avoiding explicit computation. We show (a) the conjecture is true fo
r $(h\,t) = (2\,1)$ and $p$ odd\, recovering a difficult result of Shimomu
ra and Yabe\, and (b)\nfor $h$ general and $t = h-1$\, the conjecture is t
rue "up to perfection". This is joint work with Lucas Mann\, Rin Ray\, an
d Xinyu Zhou.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART:20251117T213000Z
DTEND:20251117T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/33
DESCRIPTION:by Akhil Mathew (University of Chicago) as part of MIT Algebra
ic Topology Seminar\n\nLecture held in 2-131.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ismael Sierra Del Rio (University of Toronto)
DTSTART:20251208T213000Z
DTEND:20251208T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/34
DESCRIPTION:by Ismael Sierra Del Rio (University of Toronto) as part of MI
T Algebraic Topology Seminar\n\nLecture held in 2-131.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Spiegel (Harvard University)
DTSTART:20251201T213000Z
DTEND:20251201T223000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/35
DESCRIPTION:Title: A Classifying Space for Phases of Matrix Product Stat
es\nby Daniel Spiegel (Harvard University) as part of MIT Algebraic To
pology Seminar\n\nLecture held in 2-131.\n\nAbstract\nAlexei Kitaev has co
njectured that there should be a loop spectrum consist-\ning of spaces of
gapped invertible quantum spin systems\, indexed by spatial\ndimension
𝑑 of the lattice. Motivated by Kitaev’s conjecture\, I will detail a\
nconcrete construction of a topological space 𝐵 consisting of translati
on in-\nvariant injective matrix product states (MPS) of all physical and
bond di-\nmensions\, which plays the role of Kitaev’s space in dimension
𝑑 = 1. Hav-\ning such a space is a useful tool in the discussion of pa
rametrized phases of\nMPS\; in fact\, it allows us to define a parametrize
d phase as a homotopy class\nof maps into 𝐵.\n\nThe space 𝐵 is const
ructed as the quotient of a contractible space 𝐸 of MPS\ntensors modulo
gauge transformations. The projection map from 𝐸 to 𝐵 is\na quasifi
bration\, from which we can compute the homotopy groups of the\nclassifyin
g space 𝐵 by a long exact sequence. In particular\, 𝐵 has the weak\n
homotopy type 𝐾(ℤ\, 2) × 𝐾(ℤ\, 3)\, shedding light on Kitaev’
s conjecture in\nthe context of MPS.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American University of Sharjah\, UAE)
DTSTART:20260421T203000Z
DTEND:20260421T213000Z
DTSTAMP:20260422T225827Z
UID:MITAlgebraicTopologySeminar/36
DESCRIPTION:Title: Combinatorial Invariants of Stratified Spaces\nby
Sadok Kallel (American University of Sharjah\, UAE) as part of MIT Algebr
aic Topology Seminar\n\nLecture held in 2-132.\n\nAbstract\nWe construct a
Grothendieck ring for poset-stratified spaces and use it to compute the t
opological Euler characteristic of a number of constructions in topology a
nd geometry. This ring is defined on a suitable essentially small subcateg
ory of Top and offers a flexible real analog of the Grothendieck ring of v
arieties in algebraic geometry. A number of applications are given to orbi
folds and to spaces stratified by configuration spaces\, like chromatic co
nfiguration spaces\, bounded multiplicity configurations or finite subset
spaces.\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/36/
END:VEVENT
END:VCALENDAR