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, Teichmuller theory, hyperbolic manifolds, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields, such as algebraic geometry, mathematical physics, dynamics, geometric group theory, number theory, and topology. The triannual Ahlford-Bers colloquia serve as a venue to disseminate the relevant work to the wider mathematical community and bring the key participants together to ponder future directions in the field. The present volume includes a wide range of articles in the fields central to this legacy. The majority of articles present new results, but there are expository articles as well.
Uniformly exponential growth and mapping class groups of surfaces by J. W. Anderson, J. Aramoyona, and K. J. Shackleton An $A 1$ weight not comparable with any quasiconformal Jacobian by C. J. Bishop Curvature, stretchiness, and dynamics by M. Duchin Some special loci in the Siegel space of genus two by C. J. Earle Another approach to the automorphism theorem for Teichmuller spaces by E. Fujikawa Energy of twisted harmonic maps of Riemann surfaces by W. M. Goldman and R. A. Wentworth Isometries of some hyperbolic-type path metrics, and the hyperbolic medial axis by P. Hasto, Z. Ibragimov, D. Minda, S. Ponnusamy, and S. Sahoo From left earthquakes to right by J. Hu Small eigenvalues and maximal laminations on complete surfaces of negative curvature by C. M. Judge A generalized hyperbolic metric for plane domains by L. Keen and N. Lakic Subgroups of mapping class groups from the geometrical viewpoint by R. P. Kent, IV and C. J. Leininger Determinants of Laplacians, quasifuchsian spaces, and holomorphic extensions of Laplacians by Y.-H. Kim Hyperbolic and quasisymmetric structure of hyperspace by L. V. Kovalev and J. T. Tyson A classification of the modular transformation of infinite dimensional Teichmuller spaces by K. Matsuzaki Random hyperbolic surfaces and measured laminations by M. Mirzakhani Extensions of holomorphic motions to quasiconformal motions by S. Mitra Analyst's traveling salesman theorems. A survey by R. Schul Energy of harmonic maps and Gardiner's formla by R. A. Wentworht.