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BEGIN:VEVENT
SUMMARY:Robert Burklund (University of Copenhagen)
DTSTART:20230911T200000Z
DTEND:20230911T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/1
DESCRIPTION:Title: Beyond the telescope conjecture\nby Robert
Burklund (University of Copenhagen) as part of MIT Algebraic Topology Semi
nar\n\nLecture held in 2-131.\n\nAbstract\nThere is a natural dichotomy be
tween telescopic (T(n)-local) and chromatic (K(n)-local) homotopy theory.
Telescopic homotopy theory is more closely tied to the stable homotopy gro
ups of spheres and through them to geometric questions\, but is generally
computationally intractable. Chromatic homotopy theory is more closely tie
d to arithmetic geometry and powerful computational tools exist in this se
tting. Ravenel’s telescope conjecture asserted that these two sides coin
cide. I will present a family of counterexamples to this conjecture based
on using trace methods to analyze the algebraic K-theory of a family of K(
n)-local ring spectra beginning with the K(1)-local sphere. As a consequen
ce of this we obtain a new lower bound on the average rank of the stable h
omotopy groups of spheres. Time permitting\, I will then describe the galo
is group of the T(n)-local sphere and how this informs our understanding o
f telescopic homotopy theory. This talk is based on projects joint with Ca
rmeli\, Clausen\, Hahn\, Levy\, Schlank and Yanovski.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Antieau (Northwestern University)
DTSTART:20230918T203000Z
DTEND:20230918T220000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/2
DESCRIPTION:Title: Integral models for spaces\nby Ben Antieau
(Northwestern University) as part of MIT Algebraic Topology Seminar\n\nLec
ture held in 2-131.\n\nAbstract\nGeneralizing and building on the work of
Kriz\, Ekedahl\, Goerss\, Lurie\, Mandell\, Mathew\, Mondal\, Quillen\, Su
llivan\, Toën and Yuan\, I will describe an integral cochain model for ni
lpotent spacees of finite type. A binomial ring is a lambda-ring in which
all Adams operations act as the identity. A derived binomial ring is a der
ived Λ-ring equipped with simultaneous trivializations of the commuting A
dams operations. For example\, if X is a space\, then ZX\, the integral co
chains on X\, is naturally a derived binomial ring. The induced contravari
ant functor from spaces to derived binomial rings is fully faithful when r
estricted to nilpotent spaces of finite type. This is related\, closely\,
to recent work of Horel and of Kubrak—Shuklin—Zakharov.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hana Jia Kong (Harvard University)
DTSTART:20230925T203000Z
DTEND:20230925T220000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/3
DESCRIPTION:Title: A deformation of Borel equivariant homotopy
\nby Hana Jia Kong (Harvard University) as part of MIT Algebraic Topology
Seminar\n\nLecture held in 2-131.\n\nAbstract\nThe real motivic stable hom
otopy category has a close connection\nto the $C_2$-equivariant stable hom
otopy category. From a computational perspective\, the real motivic comput
ation can be viewed\nas a simpler version which “removes the negative co
ne” in the $C_2$-\nequivariant stable homotopy groups. On the other hand
\, by work of\nBurklund–Hahn–Senger\, one can build the completed Arti
n–Tate real\nmotivic category from the completed $C_2$-equivariant categ
ory using\nthe deformation construction associated to the $C_2$-effective
filtration.\nIn work with Gabriel Angelini-Knoll\, Mark Behrens\, and Eva
Belmont\,\nwe try to build an analog of this deformation story for a gener
al finite\ngroup $G$. We give a new interpretation of the $C_2$-effective
filtration\nin the Borel equivariant category which generalizes for $G$. U
sing this\nnew interpretation\, the deformation construction gives a defor
mation\nof the Borel equivariant stable homotopy category for general fini
te\ngroups.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Berwick-Evans (University of Illinois Urbana-Champaign)
DTSTART:20231002T203000Z
DTEND:20231002T220000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/4
DESCRIPTION:Title: Supersymmetric field theories and elliptic coho
mology\nby Dan Berwick-Evans (University of Illinois Urbana-Champaign)
as part of MIT Algebraic Topology Seminar\n\nLecture held in 2-131.\n\nAb
stract\nSince the mid 1980s\, there have been hints of a deep connection b
etween 2-dimensional field theories and elliptic cohomology. This lead to
Stolz and Teichner's conjectured geometric model for the universal ellipti
c cohomology theory of topological modular forms (TMF) in which cocycles a
re 2-dimensional supersymmetric field theories. Basic properties of these
field theories lead to expected integrality and modularity properties\, bu
t the abundant torsion in TMF has always been mysterious. In this talk\, I
will describe deformation invariants of 2-dimensional field theories that
realize some of the torsion in TMF.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Brazelton (Harvard University)
DTSTART:20231016T203000Z
DTEND:20231016T220000Z
DTSTAMP:20260404T111059Z
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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Pstrągowski (Harvard University)
DTSTART:20231023T203000Z
DTEND:20231023T220000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/6
DESCRIPTION:Title: The even filtration and prismatic cohomology\nby Piotr Pstrągowski (Harvard University) as part of MIT Algebraic Top
ology Seminar\n\nLecture held in 2-131.\n\nAbstract\nThe even filtration\,
introduced by Hahn-Raksit-Wilson\, is a canonical filtration attached to
a commutative ring spectrum which measures its failure to be even. Despite
its simple definition\, the even filtration recovers many arithmetically
important constructions\, such as the Adams-Novikov filtration of the sphe
re or the Bhatt-Morrow-Scholze filtration on topological Hochschild homolo
gy\, showing that they are all invariants of the commutative ring spectrum
alone. I will describe a linear variant of the even filtration which is n
aturally defined on associative rings and can be effectively calculated th
rough resolutions of modules\, as well as joint work with Raksit on the re
sulting extension of prismatic cohomology to the context of $E_2$-rings.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomer Schlank (Hebrew University of Jeruselam)
DTSTART:20231030T203000Z
DTEND:20231030T220000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/7
DESCRIPTION:Title: Higher Semi-additivity and Chromatically locali
zed $K$-theory\nby Tomer Schlank (Hebrew University of Jeruselam) as p
art of MIT Algebraic Topology Seminar\n\nLecture held in 2-131.\n\nAbstrac
t\nWe shall consider the functor $L_{T(n)}K $ of chromatically localized a
lgebraic $K$-theory. We shall discuss its interaction with pi-finite colim
its. This will lead to a possible alternative characterization of this fun
ctor as well as results about it's interaction with cyclotomic hyper-desce
nt. This is a key input to the proof of the telescope conjecture. This tal
k is based on joint works with Shay Ben-Moshe\, Shachar Carmeli\, and Lior
Yanovski\, as well as with Robert Burklund\, Jeremy Hahn\, and Ishan Levy
.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20231106T213000Z
DTEND:20231106T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/8
DESCRIPTION:Title: The rational homotopy groups of the $K(n)$-loca
l sphere\nby Jared Weinstein (Boston University) as part of MIT Algebr
aic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nWe compute the
rational homotopy groups of the $K(n)$-local sphere for all heights $n$ a
nd all primes $p$\, verifying a prediction that goes back to Morava in the
early 1970s. The key ingredients are (1) the Devinatz-Hopkins spectral se
quence (2) the isomorphism between the Lubin–Tate tower and the Drinfeld
tower at the level of perfectoid spaces (3) integral $p$-adic Hodge theor
y\, and (4) an integral refinement of a theorem of Tate on the Galois coho
mology of nonarchimedean fields. This is joint work with Tobias Barthel\,
Tomer Schlank\, and Nathaniel Stapleton.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Westerland (University of Minnesota)
DTSTART:20231113T200000Z
DTEND:20231113T210000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/9
DESCRIPTION:Title: Moments of L-functions via the homology of brai
d groups.\nby Craig Westerland (University of Minnesota) as part of MI
T Algebraic Topology Seminar\n\nLecture held in The seminar will meet at 3
:00 PM in Harvard Science Center SC507 at Arithmetic Statistics seminar..\
n\nAbstract\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 more geometric version when posed over function fields in positive c
haracteristic. I’ll talk about how one can reinterpret the central objec
t in this conjecture in terms of the action of the Galois group of a finit
e field on the cohomology of braid groups with certain coefficients coming
from the braid group’s interpretation as the hyperelliptic mapping clas
s group. We will see the “arithmetic factor” in this conjecture appear
in the part of this cohomology that is accessible through tools of homolo
gical stability. This is joint work with Jonas Bergström\, Adrian Diaconu
\, and Dan Petersen.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART:20231204T213000Z
DTEND:20231204T223000Z
DTSTAMP:20260404T111059Z
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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Lesh (Union College)
DTSTART:20231127T213000Z
DTEND:20231127T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/11
DESCRIPTION:Title: Normalizer decompositions of p-local compact g
roups\nby Kathryn Lesh (Union College) as part of MIT Algebraic Topolo
gy Seminar\n\nLecture held in 2-131.\n\nAbstract\nI will talk about a 'nor
malizer decomposition' for the classifying space of a p-local compact grou
p. The decomposition generalizes those of Dwyer for finite groups and of L
ibman for p-local finite groups and (separately) for compact Lie groups. I
'll show how the decomposition gives a homotopy pushout square for the exo
tic p-compact groups of Aguade and Zabrodsky by building on the example of
SU(p). This is joint work with Belmont\, Castellana\, Grbic\, and Strumil
a.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/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:20260404T111059Z
UID:MITAlgebraicTopologySeminar/12
DESCRIPTION:Title: Localizing motives and corepresentability of $
TR$ and $TC$\nby Alexander Efimov (Steklov Mathematical Institute of R
ussian Academy of Sciences and National Research University Higher School
of Economics) 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 categ
ory of localizing motives -- the target of the universal localizing invari
ant commuting with filtered colimits. The main surprising result about thi
s category is that it is rigid as a symmetric monoidal category (in the se
nse of Gaitsgory and Rozenblyum).\n \n\nAs an application of the proof of
rigidity\, we will deduce that the functors $TR$ (topological restriction)
and $TC$ (topological cyclic homology) are corepresentable in this catego
ry\, if we restrict to connective $E_1-rings$.\n\nIf time permits\, I will
explain how rigidity of $Mot^loc$ allows to construct refined versions of
(topological) Hochschild homology and its variants\, which contain much m
ore information about the $E_1-algebra$ than the usual variants of $(T)HH$
.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Belmont (Case Western Reserve University)
DTSTART:20240205T213000Z
DTEND:20240205T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/13
DESCRIPTION:Title: Computations with the modified Adams spectral
sequence\nby Eva Belmont (Case Western Reserve University) as part of
MIT Algebraic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nThe
modified Adams spectral sequence\, which computes the homotopy groups of a
Borel-equivariant spectrum\, is a combination of the homotopy fixed point
s spectral sequence and the nonequivariant Adams spectral sequence. One ca
n also use it to read off (completed) $\\mathbb{R}$-motivic homotopy group
s\, via a synthetic spectra construction. We will explain how to compute i
t 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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Angelini-Knoll (Sorbonne Paris Nord)
DTSTART:20240304T213000Z
DTEND:20240304T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/14
DESCRIPTION:Title: Syntomic cohomology of real topological $K$-th
eory\nby Gabriel Angelini-Knoll (Sorbonne Paris Nord) as part of MIT A
lgebraic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nWork of H
ahn-Raksit-Wilson extended the Bhatt-Morrow-Scholze filtration on topologi
cal cyclic homology and topological periodic cyclic homology to sufficient
ly nice ring spectra. This allows one to define syntomic cohomology and pr
ismatic cohomology at this level of generality. One example of such a nice
ring spectrum is real topological $K$-theory. In joint work with Christia
n Ausoni and John Rognes\, we compute the syntomic cohomology of real topo
logical $K$-theory modulo $(2\,η\,v_1)$. This computation produces a new
example of pure redshift and arithmetic duality. As an application\, we co
mpute the 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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen McKean (Harvard University)
DTSTART:20240311T203000Z
DTEND:20240311T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/15
DESCRIPTION:Title: Motivic Euler characteristics and power struct
ures\nby Stephen McKean (Harvard University) as part of MIT Algebraic
Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nThere is a quadrat
ic form-valued version of the compactly supported Euler characteristic com
ing from motivic homotopy. A feature of this Euler characteristic is that
it descends to a ring homomorphism out of the Grothendieck ring of varieti
es. In characteristic 0\, this Euler characteristic was constructed by Rö
ndigs and later Arcila-Maya—Bethea—Opie—Wickelgren—Zakharevich\, w
ho used Bittner’s blow up presentation of $K_0(Var)$. In characteristic
not 2\, Azouri gave a characterization in terms of the six functor formali
sm. I will discuss a hybrid approach using a sort of universal property of
$K_0(Var)$. I will then discuss power structures on $K_0(Var)$ and the Gr
othendieck—Witt ring of quadratic forms\, and conclude with a conjecture
relating these two power structures. This is joint work in progress with
Dori Bejleri\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Pstrągowski (Kyoto University)
DTSTART:20250117T213000Z
DTEND:20250117T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/16
DESCRIPTION:Title: The monochromatic Hahn-Wilson conjecture\n
by Piotr Pstrągowski (Kyoto University) as part of MIT Algebraic Topology
Seminar\n\nLecture held in 2-449.\n\nAbstract\nIn 1999\, Mark Mahowald an
d Charles Rezk introduced a class of spectra which are particularly amenab
le to understanding using the classical Adams spectral sequence\, called f
p-spectra. As first described by Rognes\, these play a pivotal role in gen
eralizing Quillen-Lichtenbaum conjectures to the setting of ring spectra.\
n\nThe Quillen-Lichtenbaum conjectures were proven for truncated Brown-Pet
erson spectra by Dylan Wilson and Jeremy Hahn in 2021\, who in this way di
scovered the first highly non-obvious example of an fp-spectrum in the for
m of algebraic $K$-theory. This led them to ask about a general structure
result for fp-spectra\, and to conjecture that they can all be built out o
f particularly simple ones.\n\nI will talk about recent joint work with Da
vid Lee where we prove a monochromatic analogue of the Hahn-Wilson conject
ure\, and deduce the original conjecture at height one.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Søren Galatius (Columbia University)
DTSTART:20250203T213000Z
DTEND:20250203T223000Z
DTSTAMP:20260404T111059Z
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 Se
minar\n\nLecture held in 2-131.\n\nAbstract\nThe general linear group of t
he integers 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”. T
he compactly supported cohomology of these spaces forms the $E_1$ page of
a spectral sequence converging to the cohomology of $BK(\\mathbb{Z})$\, th
e onefold delooping of the algebraic $K$-theory space. I will sketch how t
o construct a Hopf algebra structure on this spectral sequence\, and how i
t maps to another spectral sequence of Hopf algebras\, a version of the Co
nnes–Kreimer Hopf algebra. In recent joint work with Brown\, Chan\, and
Payne (2405.11528)\, we use this map of Hopf algebras to deduce lower boun
ds for the compactly supported cohomology of $X_n$ and of $A_n$\, the modu
li space of principally polarized abelian varieties.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Knudsen (Northeastern University)
DTSTART:20250224T213000Z
DTEND:20250224T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/18
DESCRIPTION:Title: Probabilistic invariants of finite groups\
nby Ben Knudsen (Northeastern University) as part of MIT Algebraic Topolog
y Seminar\n\nLecture held in 2-131.\n\nAbstract\nWe continue the study of
the probabilistic versions of the Lusternik–Schnirelmann category and to
pological complexity introduced in joint work with Weinberger and independ
ently by Dranishnikov–Jauhari. In the aspherical context\, where these i
nvariants are group invariants\, there is a universal upper bound in the f
inite case. We discuss progress toward calculating the exact value\, which
is equivalent to an interesting problem in equivariant homotopy theory. T
his talk is based on joint work with Shmuel Weinberger.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirai Ikebuchi (Kyoto University)
DTSTART:20250303T213000Z
DTEND:20250303T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/19
DESCRIPTION:Title: Quillen cohomology of small cartesian closed c
ategories\nby Mirai Ikebuchi (Kyoto University) as part of MIT Algebra
ic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nCohomology of L
awvere theories — small categories with finite products\, also called al
gebraic theories — is studied by Jibladze and Pirashvili. They considere
d three types of definitions\, Quillen\, Baues-Wirsching\, and Ext cohomol
ogies\, and showed that their equivalences. In this talk\, we extend their
work to small cartesian closed categories. Also\, we will briefly see its
application to logic and theoretical computer science. As Lawvere theorie
s are categorical formulation of universal algebra\, there is a famous cor
respondence between cartesian closed categories and equational theories on
simply typed lambda calculus. So\, cohomology of cartesian closed categor
ies is an invariant of such equational theories.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cary Malkiewich (Binghamton University)
DTSTART:20250331T203000Z
DTEND:20250331T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/20
DESCRIPTION:Title: Higher scissors congruence\nby Cary Malkie
wich (Binghamton University) as part of MIT Algebraic Topology Seminar\n\n
Lecture held in 2-131.\n\nAbstract\nScissors congruence is the study of po
lytopes\, up to the relation of cutting into finitely many pieces and rear
ranging the pieces. In the 2010s\, Zakharevich defined a "higher" version
of scissors congruence\, where we don't just ask whether two polytopes are
scissors congruent\, but also how many scissors congruences there are fro
m one polytope to another.\n\nZakharevich's definition is a form of algebr
aic K-theory\, which is famously difficult to compute\, but I will discuss
a surprising result that makes the computation of the higher K-groups pos
sible\, at least for low-dimensional geometries. In particular\, this give
s the homology of the group of interval exchange transformations\, and a n
ew proof 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 G
erhardt\, Mona Merling\, and Inna Zakharevich\, and also with Alexander Ku
pers\, Ezekiel Lemann\, Jeremy Miller\, and Robin Sroka.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J.D. Quigley (University of Virginia)
DTSTART:20250421T203000Z
DTEND:20250421T213000Z
DTSTAMP:20260404T111059Z
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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Senger (Harvard University)
DTSTART:20250428T203000Z
DTEND:20250428T213000Z
DTSTAMP:20260404T111059Z
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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Spitz (University of Virginia)
DTSTART:20250210T213000Z
DTEND:20250210T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/23
DESCRIPTION:Title: The Tambara Affine Line\nby Ben Spitz (Uni
versity of Virginia) as part of MIT Algebraic Topology Seminar\n\nLecture
held in 2-131.\n\nAbstract\nIn equivariant stable homotopy theory\, object
s called "Tambara functors" play the role of commutative rings. Tambara fu
nctors are abstract algebraic objects: they consist of sets with certain o
perations satisfying certain axioms\; however\, the theory of Tambara func
tors is much less developed than the theory of commutative rings\, in part
because it is not clear exactly how to define the "Tambara analogs" of ma
ny classical notions. Nonetheless\, we expect that Tambara functors admit
a theory of commutative algebra and algebraic geometry\, akin to the story
for ordinary commutative rings. In this talk\, I will discuss recent prog
ress in developing such a theory for Tambara functors – in particular\,
we prove a version of the going-up theorem\, which allows for the first co
mputation of the "affine line" in Tambara algebraic geometry. This is join
t work with David Chan\, David Mehrle\, J.D. Quigley\, and Danika Van Niel
.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART:20250505T203000Z
DTEND:20250505T213000Z
DTSTAMP:20260404T111059Z
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 Al
gebraic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nI will dis
cuss aspects of joint work with Brown\, Galatius\, and Payne. In particula
r\, we identify a Hopf algebraic structure in the weight 0 cohomology with
compact supports of the moduli space of abelian varieties\, and we deduce
exponential growth results as a corollary. A key role is played by the mo
duli space of tropical abelian varieties\, which is stratified by locally
symmetric 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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dev Sinha (University of Oregon)
DTSTART:20250310T203000Z
DTEND:20250310T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/25
DESCRIPTION:Title: From Milnor invariants to $E$-infinity cochain
structures\nby Dev Sinha (University of Oregon) as part of MIT Algebr
aic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nWe share curre
nt work which goes back and forth between geometric and algebraic topology
. We start with generalization of Milnor invariants of links\, which works
beyond where their indeterminacy limits them and extends to links any thr
ee-manifold. This generalization arises from analysis of the classical bar
construction. (So we are making progress by connecting two pieces of math
ematics developed in Fine Hall in the 1950’s.) These ideas also lead to
new algorithms to produce all polynomial functions on presented groups. We
then share recent work relating cup product to intersection product on ge
ometric cochains through vector field flows. This leads to a conjectural n
ew approach to $E$-infinity structure on cochains by “resolving partial-
definedness” rather than resolving non-commutativity. What unites these
projects is a goal of producing homotopy invariants through a combination
of tools including geometric cochains\, configuration spaces and bar const
ructions.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rok Gregoric / David Lee (John Hopkins University / MIT)
DTSTART:20250414T203000Z
DTEND:20250414T213000Z
DTSTAMP:20260404T111059Z
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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ishan Levy (University of Copenhagen)
DTSTART:20250512T203000Z
DTEND:20250512T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/27
DESCRIPTION:Title: The spectral Sullivan conjecture\nby Ishan
Levy (University of Copenhagen) as part of MIT Algebraic Topology Seminar
\n\nLecture held in 2-131.\n\nAbstract\nThe Sullivan conjecture\, proven b
y Miller in 1984\, says that the space of pointed maps from $BC_p$ to a fi
nite dimensional CW-complex is contractible. I will explain a generalizati
on of this\, where $BC_p$ can be replaced with any connected $p$-nilpoten
t infinite loop space. I will also describe some consequences and question
s surrounding this result.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Muñoz-Echániz (MIT)
DTSTART:20250915T203000Z
DTEND:20250915T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/28
DESCRIPTION:Title: A Weiss–Williams theorem for embedding space
s and an application to diffeomorphisms of solid tori\nby Samuel Muño
z-Echániz (MIT) as part of MIT Algebraic Topology Seminar\n\nLecture held
in 2-131.\n\nAbstract\nThere is a programme\, largely developed by Weiss
and Williams\, that aims to understand the homotopy type of the diffeomorp
hism group of a compact\, high-dimensional manifold $M$ in terms of Waldha
usen's algebraic $K$-theory of $M$. In this talk\, I will give a brief ove
rview of this programme and present an analogue for spaces of embeddings (
of compact manifolds $P$ into $M$\, say). The main difference with the ori
ginal programme is that the algebraic $K$-theory of $M$ is replaced by the
*relative* algebraic $K$-theory of the pair ($M\, M$ - $P$)\, which\, in
many cases\, coincides with the relative topological cyclic homology of su
ch pair — a far more computable invariant. \n\nAs an application\, I wi
ll report on ongoing joint work with João Lobo Fernandes computing ration
al homotopy 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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Behrens (University of Notre Dame)
DTSTART:20250922T203000Z
DTEND:20250922T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/29
DESCRIPTION:Title: A $C_3$-equivariant Snaith construction\nb
y Mark Behrens (University of Notre Dame) as part of MIT Algebraic Topolog
y Seminar\n\nLecture held in 2-131.\n\nAbstract\nSnaith showed that the pe
riodic complex cobordism spectrum MUP can be obtained by localizing the su
spension spectrum of BU with respect to the generator of $\\pi_2$. Chatha
m\, Hahn\, and Yuan proved analogs of this theorem where BU is replaced by
a general Wilson space. We consider the localization of the equivariant
suspension spectrum of a $C_3$-equivariant Wilson space. I will describe
work in progress which compares this spectrum to the spectrum $BP_mu3$ con
structed by Hu\, Kriz\, Somberg\, and Zou. We will revisit their construc
tion\, and flesh out some details. This represents joint work with Gabe A
ngelini-Knoll\, Max Johnson\, and Hana Jia Kong.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rok Gregoric (Johns Hopkins University)
DTSTART:20250929T203000Z
DTEND:20250929T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/30
DESCRIPTION:Title: Even periodization of spectral stacks\nby
Rok Gregoric (Johns Hopkins University) as part of MIT Algebraic Topology
Seminar\n\nLecture held in 2-131.\n\nAbstract\nIn this talk\, we will intr
oduce and discuss even periodization: an operation which approximates a sp
ectral stack as closely as possible by affines corresponding to even perio
dic ring spectra. We will discuss how this recovers and geometrizes the ev
en filtration of Hahn-Raksit-Wilson\, and how it gives rise to canonical s
pectral enhancements of versions of the prismatization stacks of Bhatt-Lur
ie and Drinfeld\, extending the approach to prismatic cohomology via topol
ogical Hochschild homology of Bhatt-Morrow-Scholze.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhouli Xu (University of California\, Los Angeles)
DTSTART:20251006T203000Z
DTEND:20251006T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/31
DESCRIPTION:Title: Proof of the existence of $\\theta_6$\nby
Zhouli Xu (University of California\, Los Angeles) as part of MIT Algebrai
c Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nThe Kervaire inv
ariant problem asks in which dimensions there exists a stably framed manif
old 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 overv
iew of the proof that $h_6^2$ survives in the Adams spectral sequence\, th
ereby resolving the final open case of the Kervaire invariant problem. I w
ill discuss new techniques involved\, some of which are inspired by motivi
c homotopy theory. This is joint work with Weinan Lin and Guozhen Wang.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20251020T203000Z
DTEND:20251020T213000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/32
DESCRIPTION:Title: On the splitting conjecture of Hopkins\nby
Jared Weinstein (Boston University) as part of MIT Algebraic Topology Sem
inar\n\nLecture held in 2-131.\n\nAbstract\nHopkins' splitting conjecture
predicts the structure of a double localization $L_{K(t)} L_{K(h)} S$ of t
he sphere spectrum\, where $K(h)$ is Morava $K$-theory at a prime $p$ and
$0 < t < h$. \nPerfectoid techniques give powerful evidence for the conje
cture while avoiding explicit computation. We show (a) the conjecture is
true for $(h\,t) = (2\,1)$ and $p$ odd\, recovering a difficult result of
Shimomura and Yabe\, and (b)\nfor $h$ general and $t = h-1$\, the conjectu
re is true "up to perfection". This is joint work with Lucas Mann\, Rin R
ay\, and Xinyu Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART:20251117T213000Z
DTEND:20251117T223000Z
DTSTAMP:20260404T111059Z
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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ismael Sierra Del Rio (University of Toronto)
DTSTART:20251208T213000Z
DTEND:20251208T223000Z
DTSTAMP:20260404T111059Z
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://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Spiegel (Harvard University)
DTSTART:20251201T213000Z
DTEND:20251201T223000Z
DTSTAMP:20260404T111059Z
UID:MITAlgebraicTopologySeminar/35
DESCRIPTION:Title: A Classifying Space for Phases of Matrix Produ
ct States\nby Daniel Spiegel (Harvard University) as part of MIT Algeb
raic Topology Seminar\n\nLecture held in 2-131.\n\nAbstract\nAlexei Kitaev
has conjectured that there should be a loop spectrum consist-\ning of spa
ces of gapped invertible quantum spin systems\, indexed by spatial\ndimens
ion 𝑑 of the lattice. Motivated by Kitaev’s conjecture\, I will detai
l a\nconcrete construction of a topological space 𝐵 consisting of trans
lation in-\nvariant injective matrix product states (MPS) of all physical
and bond di-\nmensions\, which plays the role of Kitaev’s space in dimen
sion 𝑑 = 1. Hav-\ning such a space is a useful tool in the discussion o
f parametrized phases of\nMPS\; in fact\, it allows us to define a paramet
rized phase as a homotopy class\nof maps into 𝐵.\n\nThe space 𝐵 is c
onstructed as the quotient of a contractible space 𝐸 of MPS\ntensors mo
dulo gauge transformations. The projection map from 𝐸 to 𝐵 is\na qua
sifibration\, from which we can compute the homotopy groups of the\nclassi
fying space 𝐵 by a long exact sequence. In particular\, 𝐵 has the we
ak\nhomotopy type 𝐾(ℤ\, 2) × 𝐾(ℤ\, 3)\, shedding light on Kitae
v’s conjecture in\nthe context of MPS.\n
LOCATION:https://stable.researchseminars.org/talk/MITAlgebraicTopologySemi
nar/35/
END:VEVENT
END:VCALENDAR