College of Liberal Arts & Sciences

# Algebra Seminar

**Abstract:**

Tensor-triangular geometry was initiated in the early 2000s by Paul Balmer to give a unified geometric framework for studying tensor-triangulated categories, arising in disparate areas such as modular representation theory and algebraic geometry. Given a monoidal triangulated category, this theory produces a topological space, the Balmer spectrum, which in many cases parametrizes the thick ideals of the category, and is defined in an analogous way to the spectrum of a ring. In this talk, we will consider the situation where a group G acts on a monoidal triangulated category by categorical equivalences. Example arise from group actions on schemes and group actions on Hopf algebras. We describe the relationships between the Balmer spectra of the equivariantization of the category, the crossed product of the category, and the spectrum of G-invariant ideals. This is joint work with Hongdi Huang.