Karthik Ganapathy - GL-algebras and the Noetherianity problem

Draisma recently proved that finite length polynomial representations of the infinite general linear group GL are topologically GL-noetherian, i.e., the descending chain condition holds for GL-stable closed subsets. The scheme-theoretic variant of this theorem is a major open problem in the area. I will briefly outline the rich history of this problem and provide a negative answer in characteristic two.