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SUMMARY:Robert Burklund (University of Copenhagen)
DTSTART;VALUE=DATE-TIME:20230911T200000Z
DTEND;VALUE=DATE-TIME:20230911T213000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225556Z
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;VALUE=DATE-TIME:20230918T203000Z
DTEND;VALUE=DATE-TIME:20230918T220000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225556Z
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
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SUMMARY:Hana Jia Kong (Harvard University)
DTSTART;VALUE=DATE-TIME:20230925T203000Z
DTEND;VALUE=DATE-TIME:20230925T220000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225556Z
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/
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SUMMARY:Dan Berwick-Evans (University of Illinois Urbana-Champaign)
DTSTART;VALUE=DATE-TIME:20231002T203000Z
DTEND;VALUE=DATE-TIME:20231002T220000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225556Z
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/
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BEGIN:VEVENT
SUMMARY:Thomas Brazelton (Harvard University)
DTSTART;VALUE=DATE-TIME:20231016T203000Z
DTEND;VALUE=DATE-TIME:20231016T220000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225556Z
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:Kathryn Lesh (Union College)
DTSTART;VALUE=DATE-TIME:20231023T203000Z
DTEND;VALUE=DATE-TIME:20231023T220000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225556Z
UID:MITAlgebraicTopologySeminar/6
DESCRIPTION:by Kathryn Lesh (Union College) as part of MIT Algebraic Topol
ogy Seminar\n\nLecture held in 2-131.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomer Schlank (Hebrew University of Jeruselam)
DTSTART;VALUE=DATE-TIME:20231030T203000Z
DTEND;VALUE=DATE-TIME:20231030T220000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225556Z
UID:MITAlgebraicTopologySeminar/7
DESCRIPTION:by Tomer Schlank (Hebrew University of Jeruselam) as part of M
IT Algebraic Topology Seminar\n\nLecture held in 2-131.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITAlgebraicTopologySeminar/7/
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