Course description:
Tensor triangular geometry provides a framework for doing geometry with tensor triangulated categories, in analogy to how algebraic geometry allows us to work geometrically with commutative rings. In this course, we first introduce the basic notions of tensor triangular geometry, focusing on a lattice-theoretic approach. We will then discuss how familiar notions from commutative algebras and algebraic geometry (for example descent, residue fields, the going-up theorem) generalize to the world of tt-geometry.
In the second part of the course, we examine variants of the tt-spectrum, such as the homological spectrum, as well as the resulting support theories, and develop the theory of stratification for 'big' tt-categories. Throughout, a wide range of examples will be discussed in order to illustrate the general theory and clarify the main results.
The final part of the course will touch upon some recent developments in the field. Among other things, this might include applications to representation theory and equivariant homotopy theory, taking into account the interests of the participants.
The only assumed background is familiarity with basic category theory and homological algebra. Some prior exposure to triangulated categories or higher category theory may be helpful.
Time, Date and Location: TBC