# In the Tradition of Ahlfors-Bers, VI

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*Ursula Hamenstädt; Alan W. Reid; Rubí Rodríguez; Steffen Rohde; Michael Wolf*

The Ahlfors–Bers Colloquia commemorate the
mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this
legacy lies in the fields of geometric function theory, Teichmüller
theory, hyperbolic geometry, and partial differential
equations. However, the work of Ahlfors and Bers has impacted and
created interactions with many other fields of mathematics, such as
algebraic geometry, dynamical systems, topology, geometric group
theory, mathematical physics, and number theory. Recent years have
seen a flowering of this legacy with an increased interest in their
work.

This current volume contains articles on a wide variety of subjects
that are central to this legacy. These include papers in Kleinian
groups, classical Riemann surface theory, translation surfaces,
algebraic geometry and dynamics. The majority of the papers present
new research, but there are survey articles as well.

# Table of Contents

## In the Tradition of Ahlfors-Bers, VI

- Preface vii8 free
- Plenary Talks ix10 free
- Spheres in the curve complex 112 free
- Character Varieties and Moduli of Quiver Representations 920
- 1. Introduction and Motivation 920
- 2. Moduli of 𝐺-valued Quiver Representations 1122
- 3. Character Varieties and Collapsing Arrows 1829
- 4. Strong Deformation Retractions and Pinching Vertices 2233
- 5. Super-Cyclic Quivers and Additive Quiver Representations 2839
- Appendix A. Kempf-Ness Set and Strong Deformation Retraction 3445
- References 3647

- Periodicity of asymptotic Teichmüller modular transformation 3950
- Hyperbolization of locally compact non-complete metric spaces 5162
- Quasiregular maps and the conductivity equation in the Heisenberg group 6172
- Pushing points on pillowcase covers 7788
- Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups 8798
- Continuity of Radial and Two-Sided Radial 𝑆𝐿𝐸 at the Terminal Point 101112
- No proper conjugation for quasiconvex cocompact groups of Gromov hyperbolic spaces 125136
- A differential formula for Extremal length 137148
- On convergence to the Denjoy-Wolff point in the parabolic case 153164
- Construction of a Closed Hyperbolic Surface of Arbitrarily Small Eigenvalue of Prescribed Serial Number 161172
- A simple method to compute volumes of even-dimensional Coxeter polyhedra 167178
- Some remarks about analytic functions defined on an annulus 177188
- On injectivity radius in configuration space and in moduli space 183194