Seminar on Landesman-Litt
Local systems of geometric origin over general curves
Goal
The goal of this seminar was to study recent work of Landesman-Litt on local systems of geometric origin over general curves. The main results are contained in LL22b and LL22c. We focused on the case of unipotent monodromy at the cusps to avoid the machinery of parabolic and coparabolic structures; a simplified version of the first paper is available as LL22a. The program is available as a PDF.
Schedule
| Date | Speaker | Topic | Notes |
|---|---|---|---|
| November 9 | Raju | Introduction to local systems of geometric origin | Notes |
| November 14 | Raju | Finish introduction | Notes |
| November 30 | Josh | Atiyah bundles and isomonodromic deformations | Notes |
| December 7 | Scott | The non-GGG lemma | |
| December 14 | Yichen | Prove Theorem 1.3.4 of LL22a; state Theorem 1.2.4 of LL22a | Notes |
| January 9 | Bruno | Background on CPVHS and positivity; prove Theorems 1.2.8, 1.2.4, and 1.2.6 of LL22a | Notes |
| January 11 | Raju | Introduction to MCG, MCG-finite representations, and the main theorem of LL22c | Notes |
| January 18, 25 | Vasily | Cohomology rank bound for a unitary local system on a versal family of curves | Notes |
| February 8/15 | TBA | Cohomological rigidity for canonical representations and the main theorem for unitary local systems | |
| February 15/22 | TBA | The main theorem for semisimple local systems and arithmetic applications | |
| TBA | TBA | Applications to the Putman-Wieland conjecture |
References
- [LL22a] Aaron Landesman and Daniel Litt, Isomonodromy, stability, and Hodge theory.
- [LL22b] Aaron Landesman and Daniel Litt, Geometric local systems on very general curves.
- [LL22c] Aaron Landesman and Daniel Litt, Canonical representations of surface groups.