DaFraHeiMai/GAUS-Seminar Sommersemester 2021

The P=W conjecture

Non-Abelian Hodge theory gives a real analytic isomorphism between two algebraically quite different varieties associated to a Riemann surface X: The Betti moduli space, the moduli space of representation of the fundamental group of X into a complex reductive algebraic group G and the Dolbeault moduli space, the moduli space of G-Higgs bundles on X. Analyzing the mixed Hodge structure of the character variety for G=GL(2,C) Hausel and Rodriguez-Villegas found an unexpected symmetry, the curious hard Lefschetz theorem. The P=W-conjecture asks, if this special symmetry reflects a certain structure on the Higgs bundle moduli space - the so-called Hitchin system.

We will meet on a two-weekly bases on Thursday afternoon 3.15 having two one-hour talks with a break in-between.

You can find the list of talks with the assigned speaker below. More details on individual topics can be found in the seminar program .

  1. What is P=W-conjecture about?, 22.04.21, Speaker: Organizers.
  2. The Betti moduli space, 22.04.21, Speaker: Felix Göbler.
  3. Hodge structures and mixed Hodge structures, 06.05.21, Speaker: Paul Kiefer.
  4. The mixed Hodge structure of the Betti moduli space, 06.05.21, Speaker: Matti Würthen.
  5. The de Rham moduli space and Riemann-Hilbert correspondence, 20.05.21, Speaker: Felix Röhrle.
  6. The Dolbeault moduli space and the abelian Hodge correspondence, 20.05.21, Speaker: Johannes Schwab.
  7. The Hitchin map and spectral data, 10.06.21, Speaker: Riccardo Zuffetti.
  8. Non-Abelian Hodge Correspondence, 10.06.21, Speaker: Jakob Stix.
  9. The constructible derived category and intersection complexes, 24.06.21, Speaker: Anton Güthge.
  10. Perverse sheaves and the topology of algebraic maps, 24.06.21, Speaker: Can Yaylali.
  11. P=W for tautological classes, 08.07.21, Speaker: Martin Ulirsch.
  12. P=W for G=GL(2,C), 08.07.21, Speaker: Luca Battistella.
  13. Discussion of topics for WS 2021/2022, 15.07.21