@article{MS2024,
  author = {Maulik, Davesh and Shen, Junliang},
  title = {The {$P=W$} conjecture for {$\mathrm{GL}_n$}},
  journal = {Annals of Mathematics}, volume = {200}, number = {2},
  year = {2024}, pages = {529--556}, doi = {10.4007/annals.2024.200.2.3}
}
@article{dCMS2022,
  author = {de Cataldo, Mark Andrea A. and Maulik, Davesh and Shen, Junliang},
  title = {On the {$P=W$} conjecture for {$\mathrm{SL}_n$}},
  journal = {Selecta Mathematica}, volume = {28}, year = {2022},
  pages = {90}, doi = {10.1007/s00029-022-00803-0}
}
@article{MSEndoscopy2021,
  author = {Maulik, Davesh and Shen, Junliang},
  title = {Endoscopic decompositions and the {Hausel--Thaddeus} conjecture},
  journal = {Forum of Mathematics, Pi}, volume = {9}, year = {2021},
  pages = {e8}, doi = {10.1017/fmp.2021.7}
}
@misc{HMMS2025,
  author = {Hausel, Tam{\'a}s and Mellit, Anton and Minets, Alexandre and Schiffmann, Olivier},
  title = {{$P=W$} via {$\mathcal H_2$}},
  year = {2025}, eprint = {2209.05429v2}, archivePrefix = {arXiv},
  howpublished = {\href{https://arxiv.org/abs/2209.05429v2}{arXiv:2209.05429v2}},
  url = {https://arxiv.org/abs/2209.05429v2}
}
@article{Mellit2025,
  author = {Mellit, Anton},
  title = {Toric stratifications of character varieties},
  journal = {Publications math{\'e}matiques de l'IH{\'E}S},
  volume = {142}, year = {2025}, pages = {153--240},
  doi = {10.1007/s10240-025-00158-0}
}
@article{Markman2002,
  author = {Markman, Eyal},
  title = {Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume = {544}, year = {2002}, pages = {61--82}, doi = {10.1515/crll.2002.028}
}
@article{Shende2017,
  author = {Shende, Vivek},
  title = {The weights of the tautological classes of character varieties},
  journal = {International Mathematics Research Notices},
  volume = {2017}, number = {22}, pages = {6832--6840}, year = {2017},
  doi = {10.1093/imrn/rnv363}
}
@article{HRV2015,
  author = {Hausel, Tam{\'a}s and Rodriguez-Villegas, Fernando},
  title = {Cohomology of large semiprojective hyperk{\"a}hler varieties},
  journal = {Ast{\'e}risque}, volume = {370}, year = {2015}, pages = {113--156},
  eprint = {1309.4914}, archivePrefix = {arXiv}
}
@article{dCFHLogHodge,
  author = {de Cataldo, Mark Andrea A. and Fernandez Herrero, Andres},
  title = {Geometry of the logarithmic {Hodge} moduli space},
  note = {With an appendix joint with Siqing Zhang},
  journal = {Journal of the London Mathematical Society},
  volume = {109}, number = {1}, pages = {e12857}, year = {2024},
  eprint = {2211.06754v2}, archivePrefix = {arXiv},
  doi = {10.1112/jlms.12857}
}
@misc{FHZ2025,
  author = {Fernandez Herrero, Andres and Zhang, Siqing},
  title = {Meromorphic {Hodge} moduli spaces for reductive groups in arbitrary characteristic},
  year = {2025}, eprint = {2307.16755v2}, archivePrefix = {arXiv},
  howpublished = {\href{https://arxiv.org/abs/2307.16755v2}{arXiv:2307.16755v2}},
  url = {https://arxiv.org/abs/2307.16755v2}
}
@article{HT2003,
  author = {Hausel, Tam{\'a}s and Thaddeus, Michael},
  title = {Mirror symmetry, {Langlands} duality, and the {Hitchin} system},
  journal = {Inventiones Mathematicae}, volume = {153}, year = {2003},
  pages = {197--229}, doi = {10.1007/s00222-003-0286-7}
}
@incollection{Simpson1997,
  author = {Simpson, Carlos},
  title = {The {Hodge} filtration on nonabelian cohomology},
  booktitle = {Algebraic Geometry---Santa Cruz 1995, Part 2},
  series = {Proceedings of Symposia in Pure Mathematics},
  volume = {62}, year = {1997}, pages = {217--281},
  publisher = {American Mathematical Society}
}
@article{SaitoExtension1990,
  author = {Saito, Morihiko}, title = {Extension of mixed {Hodge} modules},
  journal = {Compositio Mathematica}, volume = {74}, number = {2},
  year = {1990}, pages = {209--234},
  url = {https://www.numdam.org/item/CM_1990__74_2_209_0/}
}
@article{TubachStacks2025,
  author = {Tubach, Swann}, title = {Mixed {Hodge} modules on stacks},
  journal = {Forum of Mathematics, Sigma}, volume = {13}, year = {2025},
  pages = {e175}, doi = {10.1017/fms.2025.10122}
}
@article{TubachRealizations2025,
  author = {Tubach, Swann}, title = {On the {Nori} and {Hodge} realisations of {Voevodsky} motives},
  journal = {Compositio Mathematica}, volume = {161}, year = {2025},
  pages = {2155--2201}, doi = {10.1112/S0010437X25102431}
}
@article{dCHM2012,
  author = {de Cataldo, Mark Andrea A. and Hausel, Tam{\'a}s and Migliorini, Luca},
  title = {Topology of {Hitchin} systems and {Hodge} theory of character varieties: the case {$A_1$}},
  journal = {Annals of Mathematics}, volume = {175}, number = {3},
  year = {2012}, pages = {1329--1407}, doi = {10.4007/annals.2012.175.3.7}
}
@article{BBD1982,
  author = {Beilinson, Alexander A. and Bernstein, Joseph and Deligne, Pierre},
  title = {Faisceaux pervers},
  journal = {Ast{\'e}risque}, volume = {100}, year = {1982}, pages = {5--171}
}
@article{dCM2009,
  author = {de Cataldo, Mark Andrea A. and Migliorini, Luca},
  title = {The decomposition theorem, perverse sheaves and the topology of algebraic maps},
  journal = {Bulletin of the American Mathematical Society},
  volume = {46}, number = {4}, year = {2009}, pages = {535--633},
  eprint = {0712.0349v2}, archivePrefix = {arXiv}
}
@book{Fulton1998,
  author = {Fulton, William}, title = {Intersection Theory},
  edition = {2}, series = {Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge},
  volume = {2}, publisher = {Springer}, address = {New York}, year = {1998},
  doi = {10.1007/978-1-4612-1700-8}
}
@article{Nitsure1991,
  author = {Nitsure, Nitin}, title = {Moduli space of semistable pairs on a curve},
  journal = {Proceedings of the London Mathematical Society},
  volume = {62}, number = {2}, year = {1991}, pages = {275--300},
  doi = {10.1112/plms/s3-62.2.275}
}
@article{HRV2008,
  author = {Hausel, Tam{\'a}s and Rodriguez-Villegas, Fernando},
  title = {Mixed {Hodge} polynomials of character varieties},
  note = {With an appendix by Nicholas M. Katz},
  journal = {Inventiones Mathematicae}, volume = {174}, number = {3},
  year = {2008}, pages = {555--624}, doi = {10.1007/s00222-008-0142-x},
  eprint = {math/0612668}, archivePrefix = {arXiv}
}
@article{HLRV2011,
  author = {Hausel, Tam{\'a}s and Letellier, Emmanuel and Rodriguez-Villegas, Fernando},
  title = {Arithmetic harmonic analysis on character and quiver varieties},
  journal = {Duke Mathematical Journal}, volume = {160}, number = {2},
  year = {2011}, pages = {323--400}, doi = {10.1215/00127094-1444258},
  eprint = {0810.2076}, archivePrefix = {arXiv}
}
@article{dCMSJAMS2022,
  author = {de Cataldo, Mark Andrea and Maulik, Davesh and Shen, Junliang},
  title = {Hitchin fibrations, abelian surfaces, and the {$P=W$} conjecture},
  journal = {Journal of the American Mathematical Society},
  volume = {35}, number = {3}, year = {2022}, pages = {911--953},
  doi = {10.1090/jams/989}, eprint = {1909.11885}, archivePrefix = {arXiv}
}
@article{MSY2025,
  author = {Maulik, Davesh and Shen, Junliang and Yin, Qizheng},
  title = {Perverse filtrations and {Fourier} transforms},
  journal = {Acta Mathematica}, volume = {234}, number = {1},
  year = {2025}, pages = {1--69}, doi = {10.4310/ACTA.2025.v234.n1.a1},
  eprint = {2308.13160}, archivePrefix = {arXiv}
}
@book{Deligne1970,
  author = {Deligne, Pierre},
  title = {{\'E}quations diff{\'e}rentielles {\`a} points singuliers r{\'e}guliers},
  series = {Lecture Notes in Mathematics}, volume = {163},
  publisher = {Springer-Verlag}, address = {Berlin--New York}, year = {1970},
  doi = {10.1007/BFb0061194},
  url = {https://publications.ias.edu/sites/default/files/Number9.pdf}
}
@article{Hitchin1987SelfDuality,
  author = {Hitchin, N. J.},
  title = {The self-duality equations on a {Riemann} surface},
  journal = {Proceedings of the London Mathematical Society},
  series = {3}, volume = {55}, number = {1},
  year = {1987}, pages = {59--126}, doi = {10.1112/plms/s3-55.1.59}
}
@article{Hitchin1987Integrable,
  author = {Hitchin, Nigel},
  title = {Stable bundles and integrable systems},
  journal = {Duke Mathematical Journal}, volume = {54}, number = {1},
  year = {1987}, pages = {91--114}, doi = {10.1215/S0012-7094-87-05408-1}
}
@article{Donaldson1987,
  author = {Donaldson, S. K.},
  title = {Twisted harmonic maps and the self-duality equations},
  journal = {Proceedings of the London Mathematical Society},
  series = {3}, volume = {55}, number = {1},
  year = {1987}, pages = {127--131}, doi = {10.1112/plms/s3-55.1.127}
}
@article{Corlette1988,
  author = {Corlette, Kevin},
  title = {Flat {$G$}-bundles with canonical metrics},
  journal = {Journal of Differential Geometry}, volume = {28}, number = {3},
  year = {1988}, pages = {361--382}, doi = {10.4310/jdg/1214442469}
}
@article{Simpson1992,
  author = {Simpson, Carlos T.},
  title = {{Higgs} bundles and local systems},
  journal = {Publications math{\'e}matiques de l'IH{\'E}S}, volume = {75},
  year = {1992}, pages = {5--95}, doi = {10.1007/BF02699491}
}
@article{Deligne1971,
  author = {Deligne, Pierre},
  title = {Th{\'e}orie de {Hodge} {II}},
  journal = {Publications math{\'e}matiques de l'IH{\'E}S}, volume = {40},
  year = {1971}, pages = {5--57}, doi = {10.1007/BF02684692}
}
@article{Deligne1974,
  author = {Deligne, Pierre},
  title = {Th{\'e}orie de {Hodge} {III}},
  journal = {Publications math{\'e}matiques de l'IH{\'E}S}, volume = {44},
  year = {1974}, pages = {5--77}, doi = {10.1007/BF02685881}
}
@article{BialynickiBirula1973,
  author = {Bia{\l}ynicki-Birula, Andrzej},
  title = {Some theorems on actions of algebraic groups},
  journal = {Annals of Mathematics}, series = {2}, volume = {98}, number = {3},
  year = {1973}, pages = {480--497}, doi = {10.2307/1970915}
}
@article{HTGenerators2004,
  author = {Hausel, Tam{\'a}s and Thaddeus, Michael},
  title = {Generators for the cohomology ring of the moduli space of rank 2 {Higgs} bundles},
  journal = {Proceedings of the London Mathematical Society},
  series = {3}, volume = {88}, number = {3},
  year = {2004}, pages = {632--658}, doi = {10.1112/S0024611503014618},
  eprint = {math/0003093v2}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0003093v2}
}