The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars
Ahlfors and Lipman Bers. The core of this legacy are in the ﬁelds of geometric
function theory, Teichm¨ uller theory, hyperbolic geometry, and partial diﬀerential
equations. However their work has impacted and created interactions with many
other ﬁelds of mathematics such as algebraic geometry, dynamical systems, topol-
ogy, geometric group theory, mathematical physics, and number theory. Recent
years have especially seen a flowering of this legacy with a large number of people
entering the subject.
The Colloquia are held every three to four years to help disseminate the most
important advances to a wide mathematical audience.
The fourth Ahlfors-Bers Colloquium was held at Rutgers University-Newark in
May 2008. It attracted about 180 participants from 12 countries. In addition to
the plenary talks there were three precolloquium workshops with an emphasis on
early career mathematicians.
The 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 major-
ity of the papers present new research, but there are survey articles as well.
There have been four volumes of these Colloquia previously published by AMS
in the Contemporary Mathematics Series: volumes 211, 256, 335 and 432.