Homological stability, representation stability, and FI-modules
Introductory Workshop: Geometric Group Theory August 22, 2016 - August 26, 2016
Location: SLMath: Eisenbud Auditorium
geometric group theory
classical Lie groups
stable homotopy groups
Church-Bestvina conjecture
mapping spaces
configuration space
moduli spaces
GL(n-Z)
GL(n-R)
20Jxx - Connections of group theory with homological algebra and category theory
00A35 - Methodology of mathematics {For mathematics education, see 97-XX}
18G10 - Resolutions; derived functors (category-theoretic aspects) [See also 13D02, 16E05, 18Gxx]
18G50 - Nonabelian homological algebra (category-theoretic aspects)
14602
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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14602
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14602a.mp4
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14602b.mp4
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