Description: Spectra are ubiquitous throughout modern mathematics: The Zariski spectrum of a commutative ring, the topological spectrum representing a generalized cohomology theory, and the Balmer spectrum of a tensor-triangulated category are important instances. In each case, the spectral representation of a familiar object reveals its hidden geometry and symmetries. Amplified by modern homotopical and representation-theoretic techniques, recent years have seen a whirlwind of activity and groundbreaking progress in the development and application of spectral techniques, which may be loosely organized in the following themes:
(1) Global classification problems:
Classification of thick tensor ideals and localizing tensor ideals as the key to capturing the global structure of tensor categories; construction of novel support theories.
(2) Local-to-global principles:
Assembly and disassembly in homotopy theory and modular representation theory; adelic techniques in rational equivariant homotopy theory; reconstruction theorems in (non-)commutative algebraic geometry.
(3) Invariants, duality, and descent:
The computation of Picard groups and higher invariants like Brauer groups via descent techniques; local and global dualities.
Scientific Organizers:
- Tobias Barthel
- Paul Balmer
- John Greenlees
- Henning Krause
- Julia Pevtsova