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