Quillen stratification for tensor triangulated categories with applications to the Steenrod algebra

I will begin with some historical background on the spectrum of the cohomology ring and its significance in modular representation theory. I will then discuss Paul Balmer's approach to Quillen stratification, facilitated by his notion of the spectrum of a tensor triangulated category. Time permitting, I will then discuss an application of these methods to the problem of classifying the thick tensor-ideals of the stable category of the mod 2 Steenrod algebra.