---
OA_place: publisher
OA_type: hybrid
_id: '18970'
abstract:
- lang: eng
  text: Given a smooth projective curve C, nonabelian Hodge theory gives a diffeomorphism
    between two different moduli spaces associated to C. The first is the moduli space
    of Higgs bundles on C of rank n, which is equipped with the structure of an algebraic
    completely integrable Hamiltonian system. The second is the character variety
    of representations of the fundamental group of C into GL(n). In 2012, de Cataldo,
    Hausel, and Migliorini [1] proposed the P=W conjecture which identifies the perverse
    filtration on the cohomology of the Higgs moduli space with the weight filtration
    on the cohomology of the character variety. Recently, in 2022, two independent
    proofs of the P=W Conjecture appeared, in work of Maulik &Shen [2] and Hausel,
    Mellit, Minets &Schiffmann [6]. The aim of the Arbeitsgemeinschaft was to understand
    the P=W Conjecture and these two recent proofs.
acknowledgement: "The MFO and the workshop organizers would like to thank the\r\nNational
  Science Foundation for supporting the participation of junior researchers\r\nby
  the grant DMS-2230648, “US Junior Oberwolfach Fellows”. Moreover, the\r\nMFO and
  the workshop organizers would like to thank the Oberwolfach Foundation for supporting
  the participation of junior researchers in the Arbeitsgemeinschaft."
article_processing_charge: No
article_type: original
author:
- first_name: Tamás
  full_name: Hausel, Tamás
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
  orcid: 0000-0002-9582-2634
- first_name: Davesh
  full_name: Maulik, Davesh
  last_name: Maulik
- first_name: Anton
  full_name: Mellit, Anton
  last_name: Mellit
- first_name: Olivier
  full_name: Schiffmann, Olivier
  last_name: Schiffmann
- first_name: Junliang
  full_name: Shen, Junliang
  last_name: Shen
citation:
  ama: 'Hausel T, Maulik D, Mellit A, Schiffmann O, Shen J. Arbeitsgemeinschaft: Geometry
    and representation theory around the P=W conjecture. <i>Oberwolfach Reports</i>.
    2024;21(2):949-1004. doi:<a href="https://doi.org/10.4171/owr/2024/16">10.4171/owr/2024/16</a>'
  apa: 'Hausel, T., Maulik, D., Mellit, A., Schiffmann, O., &#38; Shen, J. (2024).
    Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture.
    <i>Oberwolfach Reports</i>. EMS Press. <a href="https://doi.org/10.4171/owr/2024/16">https://doi.org/10.4171/owr/2024/16</a>'
  chicago: 'Hausel, Tamás, Davesh Maulik, Anton Mellit, Olivier Schiffmann, and Junliang
    Shen. “Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W
    Conjecture.” <i>Oberwolfach Reports</i>. EMS Press, 2024. <a href="https://doi.org/10.4171/owr/2024/16">https://doi.org/10.4171/owr/2024/16</a>.'
  ieee: 'T. Hausel, D. Maulik, A. Mellit, O. Schiffmann, and J. Shen, “Arbeitsgemeinschaft:
    Geometry and representation theory around the P=W conjecture,” <i>Oberwolfach
    Reports</i>, vol. 21, no. 2. EMS Press, pp. 949–1004, 2024.'
  ista: 'Hausel T, Maulik D, Mellit A, Schiffmann O, Shen J. 2024. Arbeitsgemeinschaft:
    Geometry and representation theory around the P=W conjecture. Oberwolfach Reports.
    21(2), 949–1004.'
  mla: 'Hausel, Tamás, et al. “Arbeitsgemeinschaft: Geometry and Representation Theory
    around the P=W Conjecture.” <i>Oberwolfach Reports</i>, vol. 21, no. 2, EMS Press,
    2024, pp. 949–1004, doi:<a href="https://doi.org/10.4171/owr/2024/16">10.4171/owr/2024/16</a>.'
  short: T. Hausel, D. Maulik, A. Mellit, O. Schiffmann, J. Shen, Oberwolfach Reports
    21 (2024) 949–1004.
date_created: 2025-01-29T15:34:22Z
date_published: 2024-05-05T00:00:00Z
date_updated: 2025-01-29T15:39:55Z
day: '05'
ddc:
- '500'
department:
- _id: TaHa
doi: 10.4171/owr/2024/16
has_accepted_license: '1'
intvolume: '        21'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-sa/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.4171/owr/2024/16
month: '05'
oa: 1
oa_version: Published Version
page: 949-1004
publication: Oberwolfach Reports
publication_identifier:
  eissn:
  - 1660-8941
  issn:
  - 1660-8933
publication_status: published
publisher: EMS Press
quality_controlled: '1'
status: public
title: 'Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture'
tmp:
  image: /images/cc_by_sa.png
  legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode
  name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC
    BY-SA 4.0)
  short: CC BY-SA (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2024'
...