Robert Burklund: Beyond the telescope conjecture

Location

Oskar Klein auditorium (FR4), Albanova

Schedule

14:15–15:00 Pre-colloquium by Elmo Vuorenmaa  in FB54.

15:15–15:20 SMC prizes for the academic year 2023/2024 (doctoral dissertations) will be announced and awarded.
15:20–16:20 Colloquium lecture by Robert Burklund.
16:20–17:00 SMC social get together with refreshments.

Abstract

The stable homotopy groups of spheres are the basic building blocks used to construct objects in stable homotopy theory. This family of groups appear in many places throughout geometry and topology, but they remain largely mysterious. In this talk I will give a leisurely introduction to the telescope conjecture and our recent counterexample. The highlight of this work is that the same techniques allow us to give the first non-constant lower bound on the average rank of the stable homotopy groups of spheres. The talk is based on joint projects with Carmeli, Hahn, Levy, Schlank and Yanovski.