Va­ria­ti­ons on cha­rac­ter va­ri­e­tes -- Joint stu­dy group of Pa­der­born Uni­ver­si­ty and MPI Leip­zig

In this study group, we first want to get an overview of various different definitions of character varieties, the topologies on them, and the most important subspaces. Then, we contrast the “most flexible” and the “most rigid” cases: discrete and faithful or quasi-Fuchsian representations, where the character varieties are large and rich in structure, vs. examples where it is not clear if the character variety contains more than just a few isolated points. We want to focus on instructive examples, which besides the already mentioned classical quasi-Fuchsian representations, could include representations of free groups or Coxeter groups. We would also like to understand compactification techniques and their interpretation as group actions on trees or buildings.

This study group takes place since the winter term 25/26 and summer term 26:

  • Thursdays 10:50-12:00
  • Room D2-314@Uni-Paderborn
    Sophus-Lie room (A3 01)@MPI Liepzig
    as well as on Zoom

If you are interested in attending virtually, please contact one of the organizers.

A current version of the seminar program can be found here. See also the website of Jacques Audibert for further details as well as seminar notes. 

DatumSprecher/inTitel
Block I – Basics
23. Oct. 2025Jacques AudibertRepresentation varieties
30. Oct. 2025Benjamin DelarueCharacter varieties
13. Nov. 2025Jacques AudibertCharacter varieties of surface groups
Outlook – Spectral analysis
27. Nov. 2025Tobias WeichSchottky surfaces and spectral analysis
Block II – Compactification
4. Dec. 2025Jacques AudibertThe construction of Morgan–Shalen
11. Dec. 2025Carsten PetersonMorgan–Shalen compactification II: valuations and Λ-trees
18. Dec. 2025Carsten PetersonMorgan–Shalen compactification III: Λ-trees
22. Jan. 2026Xenia FlammAsymptotic cones and degenerations I
29. Jan. 2026Xenia FlammAsymptotic cones and degenerations II
5. Feb. 2026Jacques AudibertReal spectrum: algebraic preliminaries
12. Feb. 2026Xenia FlammReal spectrum: topological properties
5. March 2026Xenia FlammReal spectrum: compactification of character varieties
12. March 2026Jacques AudibertReal spectrum: actions on buildings and asymptotic cones
Block III – Quasi-Fuchsian representations
19. March 2026Samuel BronsteinQuasi-Fuchsian groups I: Basics
26. March 2026Benjamin DelarueQuasi-Fuchsian groups II: quasi-conformal maps
16. Apr. 2026Benjamin DelarueQuasi-Fuchsian groups III: quasi-conformal deformations
23. Apr. 2026Samuel BronsteinQuasi-Fuchsian space
30. Apr. 2026Jacques AudibertThe hyperbolization theorem for fibered 3-manifolds
Block IV – Resonance chains
21. May 2026Tobias WeichIntroduction to resonances on hyperbolic surfaces
28. May 2026Tobias WeichResonance chains and spectral asymptotics
11. June 2026Guenda PalmirottaNumerical resonances on Schottky surfaces: The magic behind the Selberg zeta function
18. June 2026Guenda PalmirottaNumerical resonances on Schottky surfaces: Transfer operators and resonance chains
2. July 2026Martin UlirschBerkovich Theory
t.b.a.Martin UlirschMumford Curves

Organizers:

  • Jacques Audibert (MPI Leipzig)
  • Benjamin Delarue (Uni Leipzig/Paderborn)
  • Guenda Palmirotta (Uni Paderborn)
  • Tobias Weich (Uni Paderborn)