Goal

The goal of this seminar is to study the recent work of Landesman-Litt, in particular on local systems of geometric origin over general curves. The main results are contained in LL22b and LL22c. We will focus on the case of unipotent monodromy at the cusps to avoid the machinery of (co)parabolic structures: the simplified version of the first paper may be found here: LL22a. A program may be found here.

Schedule

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 4 January 9 Bruno Background of 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. State 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, the main theorem for unitary local systems.
February 15 (22?) TBA The main theorem for semi-simple local systems and arithmetic applications.
TBA TBA Applications to the Putnam-Wieland conjecture.


References