Tuesday 23 June 2026, 16:00 - 17:00 in HG00.086
Giorgi Tigilauri (Radboud)
A model for normed algebras in rational G-spectra
The main goal of this talk is to describe normed algebras in G-spectra after rationalization. Spectra can be thought of as a homotopical generalization of abelian groups, while G-spectra are spectra equipped with symmetries coming from a group G. We will begin by explaining how G-spectra can be described in terms of diagrams of genuine fixed points connected by additive norms. For normed algebras, however, genuine fixed points interact poorly with multiplicative norms, making such a description difficult. To address this, we introduce geometric fixed points, which are better adapted to multiplicative norms. Finally, we explain how rationalization simplifies the remaining structure and allows us to describe normed algebras by means of a diagram of geometric fixed points and multiplicative norms.