Title: 

On the algebraicity of chromatic localizations of stable homotopy groups

Abstract: 

The stable homotopy groups of spheres are deceptively simple to define, yet have deep connections to diverse areas of geometry and topology and are notoriously difficult to compute. A major breakthrough in understanding these groups came with the introduction of the Adams-Novikov spectral sequence, which unveiled the chromatic perspective - a surprising bridge between stable homotopy theory and the theory of formal groups in algebraic geometry. Franke aimed to make this connection precise by conjecturing an explicit algebraic analog for the stable homotopy groups of spheres. In this talk, I will discuss the history and evolution of Franke's conjecture from its original formulation to current state of the art results.

Recording/Livestream: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=d5e864f8-e08e-4277-93cd-b19b005bb524