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I'll explain a new paper with Alexei Oblomkov where we find a filtration (which can be refined to give a composition series) of the diagonal coinvariant algebra by submodules over the x-variables using affine Schubert calculus and the homology of the affine Springer fiber. Along the way we discover a monomial basis that implies an independent proof of the Haglund-Loehr conjecture, explicit relations describing the subquotient modules, and a geometric interpretation in terms of Hessenberg varieties that we hope carries over to other root systems.