In the Tradition of Ahlfors-Bers, VI.

Intro -- Preface -- Plenary Talks -- Spheres in the curve complex -- 1. Introduction -- 2. Background -- 3. Genericity in the curve complex -- References -- Character Varieties and Moduli of Quiver Representations -- 1. Introduction and Motivation -- 2. Moduli of -valued Quiver Representations -- 3. Character Varieties and Collapsing Arrows -- 4. Strong Deformation Retractions and Pinching Vertices -- 5. Super-Cyclic Quivers and Additive Quiver Representations -- Appendix A. Kempf-Ness Set and Strong Deformation Retraction -- References -- Periodicity of asymptotic Teichmüller modular transformation -- 1. Introduction -- 2. Stable quasiconformal mapping class group -- 3. Frame of geodesics on Riemann surface -- 4. A sufficient condition for asymptotic periodicity -- 5. Asymptotic Teichmüller space -- References -- Hyperbolization of locally compact non-complete metric spaces -- 1. Introduction -- 2. Preliminaries -- 3. Hyperbolization of locally compact non-complete metric spaces -- 4. Power quasisymmetry between locally compact non-complete spaces -- Acknowledgement -- References -- Quasiregular maps and the conductivity equation in the Heisenberg group -- 1. Background material -- 2. The conductivity equation in the Heisenberg group -- 3. Conductivity solutions generate quasiregular maps -- References -- Pushing points on pillowcase covers -- 1. Preliminaries on demi-translation structures -- 2. The pillowcase -- 3. Point pushing homeomorphisms -- 4. Coverings of the pillowcase -- 5. The spine and the generalized 'L' covering. -- 6. The modified recipe -- 7. Properties of the construction -- References -- Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups -- 1. Introduction -- 2. Acknowledgements -- 3. Preliminary remarks and results -- 4. Automorphisms of nilpotent groups -- References.

Continuity of Radial and Two-Sided Radial at the Terminal Point -- 1. Introduction -- Acknowledgement -- 2. Preliminaries -- 3. Schramm-Loewner evolution ( ) -- 4. Proofs of main results -- References -- No proper conjugation for quasiconvex cocompact groups of Gromov hyperbolic spaces -- 1. Introduction -- 2. The action of isometry groups -- 3. Quasiconformal measure on the boundary of hyperbolic space -- 4. Proof of the main theorem -- 5. Proper conjugation in hyperbolic groups -- References -- A differential formula for Extremal length -- 1. Introduction -- Comparing to results in the hyperbolic geometry -- Acknowledgements -- 2. Measured laminations -- 2.1. Measured laminations -- 2.2. Piecewise linear coordinates of ℳℒ₀ -- 2.2.1. Train track -- 2.2.2. Local coordinates on ℳℒ₀ -- 3. Geodesic Hölder currents -- 3.1. The space of geodesics -- 3.2. Hölder functions and Hölder distributions -- 3.3. Transverse Hölder distributions -- 3.4. Geodesic Hölder currents -- 3.5. Geodesic currents -- 3.6. Tangent vectors to ℳℒ -- 3.7. Essential supports -- 4. Intersection number -- 4.1. Boxes and double boxes -- 4.2. Intersection number -- 4.3. Definition of intersection number : Filling measured laminations -- 4.4. Continuity -- 4.5. Differential formula for intersection number -- 5. Extremal length -- 5.1. Measured laminations on surface with punctures -- 5.2. Teichmüller theory and extremal length -- 5.2.1. Teichmüller space -- 5.2.2. Extremal length and Hubbard-Masur differentials -- 5.3. Proof of Theorem 1.1 -- 5.4. Differential in two variables -- References -- On convergence to the Denjoy-Wolff point in the parabolic case -- 1. Introduction -- 2. One-dimensional (unit disk) case -- 3. Multi-dimensional case -- References -- Construction of a Closed Hyperbolic Surface of Arbitrarily Small Eigenvalue of Prescribed Serial Number.

1. Introduction and Preliminaries -- 2. Organization of the paper -- 3. Statement and Proof of the main thorem -- 4. Application of the main theorem -- References -- A simple method to compute volumes of even-dimensional Coxeter polyhedra -- 1. Introduction -- 2. Coxeter polyhedra and diagrams -- 3. Euler characteristic and volume -- 4. Examples -- References -- Some remarks about analytic functions defined on an annulus -- 1. Introduction -- 2. Proof of Theorem 1.1 -- 3. Consequences of the serial rule -- 4. From area to capacity -- 5. Principal frequency -- References -- On injectivity radius in configuration space and in moduli space -- 1. Introduction -- 2. Preliminaries and main results -- 3. Proof of Theorem 2.1 -- 4. Proof of Theorem 2.2 -- References.

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