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SUMMARY:Integral Models for Spaces via the higher Frobenius
DTSTART:20200922T170000
DTEND:20200922T180000
DTSTAMP:20260511T081151Z
UID:443f6e05e8209bb5b84715dae28f7bd5569a7cac0e70978a9578ad65
CATEGORIES:Conferences - Seminars
DESCRIPTION:Allen Yuan\, Massachusetts Institute of Technology\nWe will de
 scribe a fully faithful integral model for spaces in terms of their E-infi
 nity algebras of cochains which assembles Mandell's p-adic homotopy theory
  with Sullivan's rational homotopy theory.  The key input is the developm
 ent of a homotopy coherent Frobenius action on a certain subcategory of p-
 complete E-infinity-rings for each prime p. Using this action\, we will se
 e that the data of a space X is the data of its E-infinity-algebra of sphe
 rical cochains together with a trivialization of the Frobenius action afte
 r completion at each prime.  \n\nWe will then outline the construction of
  this Frobenius action. This involves constructions in equivariant homotop
 y theory\, which produce an action of Quillen's Q-construction (on the cat
 egory of abelian groups) on certain E-infinity-rings with ``genuine equiva
 riant multiplication."  The second main idea is a ``pre-group-completed" 
 variant of algebraic $K$-theory\; we will state some basic results about t
 his ``partial K-theory" and briefly discuss the partial K-theory of F_p.
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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