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VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Topology Seminar: Rational Parametrised Stable Homotopy Theory
DTSTART:20180612T151500
DTEND:20180612T161500
DTSTAMP:20260511T142815Z
UID:83a2f238f1d3d4151ba8a62d5cd06efd6680062254aeb76f6ef1fc16
CATEGORIES:Conferences - Seminars
DESCRIPTION:Vincent Braunack-Mayer (University of Zurich)\nRational homoto
 py theory is a simplification of homotopy theory in which all torsion phen
 omena are systematically ignored. Under some mild hypotheses\, celebrated 
 results of Quillen and Sullivan provide complete descriptions of the ratio
 nal homotopy category in terms of algebraic data. Quillen's approach ident
 ifies the rational homotopy type of a 1-connected space with a dg coalgebr
 a or\, equivalently\, with a dg Lie algebra\, whereas Sullivan's approach 
 identifies the rational homotopy theory of nilpotent spaces of finite type
  with finite type cochain algebras. Stably\, the situation is much simpler
 : the stable rational homotopy category is identified with graded rational
  vector spaces.\n\nIn this talk\, I present recent results on the rational
  homotopy theory of parametrised spectra which unify these established mod
 els for stable and unstable rational homotopy theory. A parametrised spect
 rum is a family of spectra parametrised by a fixed parameter space\, repre
 senting a cohomology theory twisted by an unstable homotopy type. After di
 scarding torsion\, I demonstrate that both Quillen's and Sullivan's approa
 ches to rational homotopy theory can be lifted to provide algebraic charac
 terisations of the rational homotopy category of spectra parametrised by a
  1-connected space. The underlying idea is that whereas a parametrised X-s
 pectrum P is a family of spectra twisted by or acted upon by X\, after dis
 regarding torsion this becomes the information of a graded rational vector
  space acted upon by an algebraic avatar of X.\n\nI conclude by discussing
  an application of these results to M-theory\, where we obtain a rational 
 lift to M-theory of the twisted K-theory classification of D-brane charges
  in 10-dimensional superstring theory.
LOCATION:MA A1 12 https://plan.epfl.ch/?room=MAA112
STATUS:CONFIRMED
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