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Homological stability, representation stability, and FI-modules

Introductory Workshop: Geometric Group Theory August 22, 2016 - August 26, 2016

August 26, 2016 (11:00 AM PDT - 12:30 PM PDT)
Speaker(s): Thomas Church (Stanford University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • geometric group theory

  • classical Lie groups

  • stable homotopy groups

  • Church-Bestvina conjecture

  • mapping spaces

  • configuration space

  • moduli spaces

  • GL(n-Z)

  • GL(n-R)

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14602

Abstract

Homological stability is the classical phenomenon that for many natural families of moduli spaces the homology groups stabilize. Often the limit is the homology of another interesting space; for example, the homology of the braid groups converges to the homology of the space of self-maps of the Riemann sphere. Representation stability makes it possible to extend this to situations where classical homological stability simply does not hold, using ideas inspired by asymptotic representation theory. I will give a broad survey of homological stability and a gentle introduction to the tools and results of representation stability, focusing on its applications in topology.

 

Supplements
26653?type=thumb Church Notes 160 KB application/pdf Download
Video/Audio Files

14602

H.264 Video 14602a.mp4 298 MB video/mp4 rtsp://videos.msri.org/data/000/026/481/original/14602a.mp4 Download
H.264 Video 14602b.mp4 206 MB video/mp4 rtsp://videos.msri.org/data/000/026/482/original/14602b.mp4 Download
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