Homological stability, representation stability, and FI-modules
Introductory Workshop: Geometric Group Theory August 22, 2016 - August 26, 2016
Location: MSRI: Simons Auditorium
geometric group theory
classical Lie groups
stable homotopy groups
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
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.
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