Intercity Geometry Seminar 2020    
Perverse filtrations, Hilbert schemes,    
and the P=W conjecture for parabolic Higgs bundles    
after Junliang Shen and Zili Zhang    

Some references

The $P=W$ was originally conjectured by de Cataldo, Hausel and Migliorini ( arXiv link). This original paper provide a proof in the case of rank 2 bundles. The recent papers of Junliang Shen and co-authors prove the conjecture in different set-ups using the combinatorics of tautological classes of Hilbert schemes of points: moduli spaces of parabolic bundles (subject of the seminar, arXiv link), genus 2 curves ( arXiv link), and an analogue of the conjecture for compact hyper-kaehler manifolds ( arXiv link).

Videos and notes of the talks

The videos of the first talks will be uploaded on a private youtube channel. Send an email to your local organisers to obtain the link to these videos.

Some notes of the talks.

Higgs bundles and the non-abelian Hodge correspondence, by Lenny Taelman pdf.
Introduction to perverse sheaves, by Lie Fu pdf.