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Representation stability. (English) Zbl 1373.55006
Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. II: Invited lectures. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-805-6/hbk; 978-89-6105-803-2/set). 1173-1196 (2014).
Summary: Representation stability is a phenomenon whereby the structure of certain sequences \(X_n\) of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a framework, the theory of FI-modules, that explains the mechanism behind it.
For the entire collection see [Zbl 1314.00104].

55N99 Homology and cohomology theories in algebraic topology
55R80 Discriminantal varieties and configuration spaces in algebraic topology
14F20 √Čtale and other Grothendieck topologies and (co)homologies
11T06 Polynomials over finite fields
Full Text: arXiv