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Equivariant Operadic Algebras

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, I'll describe the basics of a family of equivariant operads which generalize the classical notion of an \(E_\infty\) operad. These \(N_\infty\) operads parameterize multiplications in which the group action is intermingled with the ordering of the coordinates, explaining some of the exciting peculiarities that arise in equivariant homotopy theory. This talk will have an introductory feel to it, and I'll discuss more generally how maps into an operad give rise to natural operations on the algebras over it, and then specialize to the case of \(N_\infty\) operads and equivariant infinite loop spaces. Time permitting, I will also sketch out how a similar story holds motivically.

Mathematics; Algebraic topology; Category theory; homological algebra

video/mp4

Author affiliation: University of California Los Angeles

2016-11-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59765

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/