Thomas Nikolaus - Frobenius homomorphisms in higher algebra (ICM 2022)

Talk given for the International Congress of Mathematicians 2022 at the "Geometry and Topology, ICM sectional workshop" in Copenhagen.

Abstract:
We will discuss instances of Frobenius homomorphisms in homotopy theory. Similar to ordinary algebra, these morphism play an important role in higher algebra and are related to various concepts in stable homotopy theory and algebraic K-theory. We also discuss the notion of perfectness, which is to say that these morphisms are equivalences, and relate this notion to the Segal conjecture, the red-shift conjecture and the classification of spaces by stable data. We also present new calculations of K-theory groups based on those ideas.

The slides are available on my webpage