abstract-isaac-sasha

The homological spectrum is a topological space attached to a rigid tt-category that realises the Balmer spectrum as its Kolmogorov quotient. I will explain how one can obtain the homological, and thus Balmer, spectrum through the Ziegler spectrum and use this approach to motivate the introduction of the Shift homological spectrum. This is a topological space defined for any (compactly generated) triangulated category. I will give examples and relate it to the Ziegler spectrum. I will then show how, in the case of a tt-category, the original homological spectrum relates to the shift homolgical spectrum. This talk is based on joint work with J. Williamson and A. Zvonareva.

Building on the connection between the Balmer spectrum and homological spectrum discussed in the talk by Bird, I will introduce a topological space that parametrises certain thick subcategories of compact objects of a compactly generated triangulated category. I will discuss the connection between this topological space and the space of rank functions (and thus endofinite objects). I will give examples when every thick subcategory can be obtained from this space. The talk is based on joint work in progress with Isaac Bird and Jordan Williamson.