Speaker: Kaya Arro – University of California Riverside
Abstract: Representation stability is a regularity property enjoyed by the homology of many naturally arising objects indexed by the category of finite sets and injections. It turns out, any such FI-object in a presentable stable $\infty$-category admits a Taylor tower of approximations by representation stable FI-objects. From this Taylor tower, one obtains Taylor coefficients as well as natural transformations between these coefficients, and, assuming the vanishing of a Tate construction (satisfied e.g. when working rationally), it is possible to reconstruct a Taylor tower from these coefficients and natural transformations.