An introduction to tensor triangular geometry

Tensor triangulated categories arise in a truly diverse range of mathematical disciplines, from algebraic geometry and modular representation theory to stable homotopy theory, symplectic topology, functional analysis, and beyond. Tensor triangular geometry is a recent theory --- initiated and developed by Paul Balmer and his collaborators --- which studies tensor triangulated categories geometrically via methods motivated by algebraic geometry.

Successes of the theory include applications to equivariant stable homotopy theory and the introduction of descent methods to modular representation theory. A key tool for these applications has been a tensor triangular analogue of the étale topology, and the surprising fact that in equivariant contexts, restriction to a subgroup can be regarded as an étale extension.

In this talk, I will give an introduction to this area of mathematics, with an emphasis on the big picture.

About the speaker

Beren Sanders is Assistant Professor in the Mathematics Department at UC Santa Cruz. Previously, he was a postdoc at EPFL and at the University of Copenhagen. He completed his PhD at UCLA under the supervision of Paul Balmer