Speaker: Jack Davies ，Bergische Universität Wuppertal

Inviter: 邹佛灵

Title: Detection methods with synthetic spectra

Language: English

Time & Venue: 2025.11.17 16:00-17:00 Zoom: 6817169181 Password: 211748

Abstract: The use of synthetic (or motivic or filtered or...) spectra for studying spectral sequences from a homotopical perspective has been a major theme in many recent computations in the stable homotopy groups of spheres. In this talk, I would like to discuss some basic tools and techniques for using synthetic spectra, paired with a detection spectrum X, like real K-theory or topological modular forms, together with some operations on X, to produce infinite periodic families in the stable homotopy groups of spheres. In particular, we want to focus on the utility of the synthetic Hurewicz image of X to detect these families in the classical stable homotopy groups of spheres. We will begin with the height one example of real K-theory together with its natural Adams operations in some detail, before moving onto various generalisations at height 2. If there is time, we will comment on some more recent advances. This is all joint work with Christian Carrick.