The mathematical works of Lars Ahlfors and Lipman Bers are fundamental and lasting. They have influenced and altered the development of twentieth century mathematics. The personalities of these two scientists helped create a mathematical family and have had a permanent positive effect on a whole generation of mathematicians. Their mathematical heritage continues to lead succeeding generations. In the fall of 1994, one year after Bers' death, some members of this family decided to inaugurate a series of conferences, The Bers Colloquium, to be held every three years. The theme was to be a topic in the Ahlfors-Bers mathematical tradition, broadly interpreted. Ahlfors died a year after the first colloquium; future colloquia in this series will be called ""The Ahlfors-Bers Colloquium"".The first colloquium was held in October 1995 at the Graduate Center, CUNY in New York. It coincided roughly with the second anniversary of Bers' death. There were six lectures and much informal mathematical discussion. This volume contains papers by the speakers and many of the participants. The broad range of papers indicates how strong and far-reaching Bers' influence has been. The topics represented in the book include Teichmuller theory, Kleinian groups, higher dimensional hyperbolic geometry, geometry of numbers, circle packings, theory of discrete groups, classical complex function theory, one dimensional dynamics, fluid dynamics, quasiconformal mappings in higher dimensions, partial differential equations, and classical algebraic geometry. This title features: twenty-seven very high-level papers on related topics, open problems, and expository articles.
Computing the Douady-Earle extension by W. Abikoff and T. Ye Selected problems in Kleinian groups and hyperbolic geometry by A. Basmajian The law of the iterated logarithm for Kleinian groups by C. J. Bishop and P. W. Jones Weil-Petersson geometry and determinant bundles on inductive limits of moduli spaces by I. Biswas and S. Nag Iteration of mapping classes on a Bers slice: examples of algebraic and geometric limits of hyperbolic 3-manifolds by J. F. Brock Lattice constants and a lemma of Zagier by C. Cao, F. W. Gehring, and G. J. Martin The quasi-Fuchsian space of four-punctured spheres by Y. Chiang Approximating $L^2$ invariants of amenable covering spaces: A heat kernel approach by J. Dodziuk and V. Mathai Random walks on circle packings by T. Dubejko Some maximal holomorphic motions by C. J. Earle Vector fields for holomorphic motions of closed sets by C. J. Earle, F. P. Gardiner, and N. Lakic Theta constant identities with applications to combinatorial number theory by H. M. Farkas and I. Kra The topology of real projective structures by D. M. Gallo A discreteness condition for subgroups of $PSL(2,{\mathbfC})$ by J. Gilman On principally polarized abelian varieties and Riemann surfaces associated to prisms and pyramids by V. Gonzalez-Aguilera and R. E. Rodriguez Schur products of certain polynomials by A. Hinkkanen Inverse problems for fluid flows with a moving boundary by Y. E. Hohlov and D. Y. Kleinbock On rigidity of one-dimensional maps by Y. Jiang Twist maps and Aubry-Mather sets by Y. Katznelson and D. S. Ornstein How to bend pairs of punctured tori by L. Keen and C. Series Lipman Bers, complex analyst by I. Kra and B. Maskit Strebel points by N. Lakic Remarks on $m$-symmetric Riemann surfaces by B. Maskit Quasi-conformal mappings of Carnot-Caratheodory spaces by G. D. Mostow Lipman Bers and partial differential equations by L. Nirenberg Irrational rotations by D. J. Pinchbeck $\mu$-homeomorphisms by U. Srebro and E. Yakubov.
