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SUMMARY:Shachar Carmeli (Weizmann Institute of Science)
DTSTART:20210719T140000Z
DTEND:20210719T150000Z
DTSTAMP:20260423T004733Z
UID:MITTop/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITTop/37/">
 Higher semiadditivity and the K(1)-local sphere</a>\nby Shachar Carmeli (W
 eizmann Institute of Science) as part of MIT topology seminar\n\n\nAbstrac
 t\nHigher semiadditivity is a property of an infinity-category that allows
 \, in particular\, for the summation of families of morphisms between obje
 cts parametrized by pi-finite spaces.\n\nHopkins and Lurie showed that the
  K(n)-localizations of the infinity category of spectra are higher semiadd
 itive. Consequently\, by a work of Harpaz\, the mapping objects in these i
 nfinity-categories admit the rich structure of higher commutative monoids.
 \nWhile many abstract properties of these higher commutative monoids are k
 nown\, not many explicit computations of them have been carried out so far
 .\n\nIn my talk\, I will present a work in progress\, joint with Allen Yua
 n\, which aims to completely determine this higher commutative monoid stru
 cture of the K(1)-local sphere. Specifically\, I will show how to use high
 er semiadditive versions of algebraic K-theory and Grothendieck-Witt theor
 y to compute the summation maps along groupoids for the K(1)-local sphere.
   At the prime 2\, this allows us to realize some non-trivial classes in i
 ts homotopy groups as semiadditive cardinalities of pi-finite spaces\, and
  to compute explicitly certain power operations that arise from the higher
  semiadditivity.\n
LOCATION:https://researchseminars.org/talk/MITTop/37/
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