Stratifying phases of matters

Stratification theory has many applications in geometry and homotopy theory, from singularity theory to genuine G spectra. Recently, the theory of stratifying categories provides a uniform way to construct constructible sheaves: local systems on each stratum together with linking data between the links (and higher coherences). We take this perspective and stratify the constructive sheaves of phases of matter. Even in quantum mechanics, we get surprisingly mathematical and physics results. In this talk we will focus on the math part, and see how we can get the Borel-Weil theorem for free. If time allows, I will describe more mathematics and physics applications. This is joint work with Ryan Thorngren.