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SUMMARY:Large Scale Open Subsets of Configuration Spaces and the Foundatio
 ns of Factorization Homology
DTSTART:20210222T171500
DTEND:20210222T181500
DTSTAMP:20260510T025402Z
UID:1824672b4339637243c79307d85e1df77104803a758a3663c433b498
CATEGORIES:Conferences - Seminars
DESCRIPTION:Michael Mandell\, Indiana University\nThis project (joint with
  Andrew Blumberg) aims to adapt the foundations of factorization homology 
 to be more amenable to equivariant generalizations for actions of positive
  dimensional compact Lie groups. This requires finding replacements for ar
 guments that discretize configuration spaces (e.g.\, arguments in terms of
  quasi-categories) or that use a local-to-global approach (arguments in te
 rms of a small neighborhood of a point in a configuration space).  In pra
 ctice\, each such theorem reduces (by a Quillen Theorem A argument) to sho
 wing that a comparison map from a certain homotopy coend (that depends on 
 the specifics of  the statement) to a configuration space (or related spa
 ce) is a weak equivalence\; the replacement strategy is to construct a cov
 er of the configuration space by "large scale" open subsets whose intersec
 tion combinatorics and homotopy types mirror those of the composition comb
 inatorics and homotopy types in a bar construction for the homotopy coend.
   ("Large scale" is descriptive rather than technical: the game to is to 
 describe open subsets of configuration spaces C(n\,M) that will be G-stabl
 e when M=G/H is an orbit space for a positive dimensional compact Lie grou
 p G.)  In other words\, the project is to deduce the properties of factor
 ization of homology directly from "large scale" open covers of configurati
 on spaces.
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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