Workshop: Spectra, triangles, and higher structures

Dates: December 05 - 09, 2022
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: Paul Balmer (UCLA), Tobias Barthel (Bonn), Paul Goerss (Northwestern), Markus Linckelmann (London), Julia Pevtsova (UW)



The related concepts of infinity-categories and tensor triangulated categories have many antecedents and core examples in algebraic topology, algebraic geometry, and representation theory. These include categories built from sheaves, from group representations, from classical spectra in spaces, and all the ways these ideas can be mixed and matched. The last fifteen years have seen the  emergence of new fields where these ideas apply, the extension of classical ideas to these new areas, the revelation of unexpected new structures, an explosion of new techniques, and applications to unexpected areas of mathematics quite a long way from the roots.

The aim of this workshop is to build on these developments and to highlight recent new results. This will include lectures in derived algebraic geometry, motivic homotopy theory, tensor-triangular geometry in its various guises, representation theory, and related areas of commutative algebra, algebraic models, functor categories, and stable module category theory. We hope to emphasize the connections between these lines of thought, to highlight the ways in which old problems led to new ideas, and to see how the new directions in turn shed new light on the classical problems.