Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture

  • Tamas Hausel

    Institute of Science and Technology Austria (IST Austria), Klosterneuburg, Austria
  • Davesh Maulik

    Massachusetts Institute of Technology, Cambridge, USA
  • Anton Mellit

    Universität Wien, Wien, Austria
  • Olivier Schiffmann

    Université de Paris-Saclay, Orsay, France
  • Junliang Shen

    Yale University, New Haven, USA
Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture cover
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Abstract

Given a smooth projective curve , nonabelian Hodge theory gives a diffeomorphism between two different moduli spaces associated to . The first is the moduli space of Higgs bundles on of rank , 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 into . In 2012, de Cataldo, Hausel, and Migliorini [1] proposed the 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 Conjecture appeared, in work of Maulik &Shen [2] and Hausel, Mellit, Minets &Schiffmann [6]. The aim of the Arbeitsgemeinschaft was to understand the Conjecture and these two recent proofs.

Cite this article

Tamas Hausel, Davesh Maulik, Anton Mellit, Olivier Schiffmann, Junliang Shen, Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture. Oberwolfach Rep. 21 (2024), no. 2, pp. 949–1004

DOI 10.4171/OWR/2024/16