Friday, February 21, 7.527
Isaac Bird (Charles University, Prague), The shift spectrum and topologising rank functions.

Abstract:
I will introduce the shift spectrum, which is a topological space associated to any compactly generated triangulated categories. I will then show how this space can be used to classify a family of thick subcategories of the compact objects. I will discuss how to compute this space, explain its relationship to the Ziegler spectrum, and show that it can be used to parametrise all kernels of integral rank functions. I will then compare this space to the Balmer spectrum from tensor-triangular geometry, and explain how the shift spectrum could be considered as a non-monoidal analogue. This will be based on joint work with J. Williamson and A. Zvonareva.