Perverse filtrations, Hilbert schemes, and the P=W conjecture for parabolic Higgs bundles

Junliang Shen, Zili Zhang

We prove de Cataldo-Hausel-Migliorini's P=W conjecture in arbitrary rank for parabolic Higgs bundles labeled by the affine Dynkin diagrams ${\tilde{A}}_0$, ${\tilde{D}}_4$, $\tilde{E}_…