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Representation stability and finite linear groups

4:00 pm Thursday, January 29, 2015
Steven Sam (UC Berkeley)

Abstract: Homological stability is the phenomenon in which the homology of a sequence of objects eventually becomes constant; representation stability is a generalization of this phenomenon when the objects have group actions. This was recently studied by Church, Ellenberg, Farb, Nagpal for symmetric groups. I will give an introductory overview of this and then discuss recent joint work with Andrew Putman in which the groups are finite linear groups like SLn(Z/ℓ) and the objects are congruence subgroups of various kinds. The techniques use ideas from commutative algebra and topology but I will try to keep the technicalities to a minimum.

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