Bonn Topology Group - Abstracts

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Talk

November 19, 2024
Maxime Ramzi (Universität Münster): Polynomial functoriality of localizing invariants

Abstract

Algebraic K-theory is naturally seen as a functor on stable oo-categories and exact functors between them. However it was realized some time ago that it carries more functoriality, namely it is functorial in polynomial functors between stable oo-categories, and this extra functoriality is helpful in setting up some extra structure such as Adams operations. In this talk, I will discuss how the Barwick-Glasman-Mathew-Nikolaus approach to this functoriality can be rephrased in terms of an explicit comonadic approach; and I will discuss how this explicit comonadic approach can in turn be used to refine the polynomial functoriality of algebraic K-theory to take values in "polynomial maps of spectra". If time permits, I will also discuss applications to TR and TC. This talk is based on joint work with Thomas Blom and Thomas Nikolaus.