article published yes Tamás Hausel author 4A0666D8-F248-11E8-B48F-1D18A9856A870000-0002-9582-2634 Davesh Maulik author Anton Mellit author Olivier Schiffmann author Junliang Shen author TaHa department 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. https://creativecommons.org/licenses/by-sa/4.0/ EMS Press2024 eng 1660-8933 1660-894110.4171/owr/2024/16 212949-1004 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> T. Hausel, D. Maulik, A. Mellit, O. Schiffmann, J. Shen, Oberwolfach Reports 21 (2024) 949–1004. 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>. 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. 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> 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>. 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. 189702025-01-29T15:34:22Z2025-01-29T15:39:55Z