Perverse sheaves on varieties with large fundamental group

Reading Group at TU Chemnitz, Winter 2025/26

Time and Venue

Time	Mondays 10:00 - 11:30
Venue	Hybrid via Zoom
Registration	Send an email to kraet@mathematik.tu-chemnitz.de for the zoom link

Program

The topic of this reading group is a preprint by Deng and Wang about the linear Hopf-Thurston conjecture [arxiv:2405.12012]: Based on earlier work of Arapura and Wang [arxiv:2109.07887], they show that on any smooth complex projective variety whose fundamental group admits a large representation over a field, all perverse sheaves have nonnegative Euler characteristic.

You can find a preliminary program here: Program

The recordings from the lectures can be found here: Videos

Notes from the lectures will be posted in the schedule below after each lecture.

Tentative schedule

10.11.2025	Introduction and Overview (Thomas Krämer) [Notes]
24.11.2025	Multivalued 1-forms and nearby cycles (Christian Sevenheck) [Notes]
01.12.2025	Positivity from period maps (Christian Lehn) [Notes]
08.12.2025	Proof of the Hopf-Thurston conjecture: Characteristic p (Fei Ren)
19.01.2026	Proof of the Hopf-Thurston conjecture: Characteristic 0 (Constantin Podelski)
26.01.2026	Harmonic maps into buildings (Xiaoxiang Zhou)
02.02.2026	Spectral covers (TBA)

Some References

Y. Deng and B. Wang, Linear Chern-Hopf-Thurston conjecture.
D. Arapura and B. Wang, Perverse sheaves on varieties with large fundamental group.
Y. Deng and K. Yamanoi, Linear Shafarevich conjecture in positive characteristic.
Y. Deng, K. Yamanoi and L. Katzarkov, Reductive Shafarevich Conjecture.
P. Eyssidieux, Lectures on the Shafarevich conjecture on uniformization.