Abstract

In this talk l will provide a brief summary of tensor triangulated geometry as initiated by Balmerand l will discuss a number of interactions and potential research directions in algebraic geometryOur interest lies in understanding the different tensor structures one can equip the derived categoryof a variety with, and how this guestion reflects the geometry of the space in the same fashion asthe study of Fourier-Mukai partners. Additionally we will discuss the use of higher category theory toapproach this problem and provide a result describing spaces of tensor structures with certain fixeddata.