The 2001 Ahlfors-Bers Colloquium was held at the University of Connecticut
in Storrs from October eighteenth through the twenty-first, while the leaves red-
dened and fell from the trees. It was the most recent of the nearly half century of
conferences in and around the mathematical school led, for many years, by Lipman
Bers and Lars Ahlfors. They started a tradition based on profound mathematics
coupled with scholarship, wide-ranging interests and personal involvement. The
core about which this tradition unfolded is the geometric function theory which
can be traced back
to the work of Riemann, Klein, Poincare and Koebe. Over the
years the scope of the conferences has broadened into diverse areas of mathematics
either feeding from or having roots in this core discipline.
The Colloquium was held about a month after the tragic events of September
11, 2001. Air transportation was a mess and was felt by many to be chaotic and
fraught with imminent peril. A number of the people who had planned to attend
did not come. The hotel on campus was new and barely ready for occupation-
in fact, the first person to register was Albert Marden who was a participant in
the Colloquium. Despite the difficulties, about 130 people gathered in Storrs for
the long weekend. The colloquium had thirty-four talks delivered in three work-
shops and eleven plenary lectures. Many of the talks presented by participants are
documented in this volume.
Some of the speakers were new to mathematics conferences while others were
veterans of earlier meetings in which Ahlfors and Bers had been active participants
and leaders. The contacts made between the mathematical generations resulted in
collaborations which have proved extremely productive.
These proceedings carry the number three. There were no volumes numbered
one or two, although the second in this series had the same title without a number.
This volume documents the third Colloquium: the third since the passing of Lipman
Bers and the second since the death of Lars Ahlfors.
The organizing committee for the Colloquium consisted of William Abikoff
(chair), Ara Basmajian, Richard Canary, Clifford Earle, Frederick Gardiner, Fred-
erick Gehring, Andrew Haas, Irwin Kra, Albert Marden and Bernard Maskit.
For the organizers, it is rewarding to have seen both the depth and breadth of
the talented younger people entering our field. Their participation in the Colloquia
energizes and invigorates the Ahlfors-Bers tradition.