Describing the thick ideals of a monoidal triangulated category is a key component of the analysis of the category. We will show how this can be done by non-commutative tensor triangular geometry (NTTG), thus extending the celebrated Balmer’s theorem from the symmetric case. We will then use NTTG to analyse the stable categories of finite tensor categories, which play an important role in representation theory, mathematical physics and quantum computing. We will present general results linking this approach to the traditional one through cohomological support, based on a notion of categorical centers of cohomology rings of monoidal triangulated categories.
This is joint work with Daniel Nakano (Univ Georgia) and Kent Vashaw (MIT).
This video is part of the conference Representation Theory and Geometry that took place at the University of Georgia.
