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Product Code:  CONM/211 
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Electronic ISBN:  9780821878033 
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Book DetailsContemporary MathematicsVolume: 211; 1997; 479 ppMSC: Primary 30; 32; 35;
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 AhlforsBers mathematical tradition, broadly interpreted. Ahlfors died a year after the first colloquium; future colloquia in this series will be called The AhlforsBers 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 farreaching Bers' influence has been. The topics represented in the book include Teichmüller 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.
Features: Twentyseven very highlevel papers on related topics
 Open problems
 Expository articles
ReadershipGraduate students and research mathematicians interested in functions of a complex variable, and related areas of mathematics.

Table of Contents

Articles

William Abikoff and Taiping Ye  Computing the DouadyEarle extension [ MR 1476978 ]

Ara Basmajian  Selected problems in Kleinian groups and hyperbolic geometry [ MR 1476979 ]

Christopher J. Bishop and Peter W. Jones  The law of the iterated logarithm for Kleinian groups [ MR 1476980 ]

Indranil Biswas and Subhashis Nag  WeilPetersson geometry and determinant bundles on inductive limits of moduli spaces [ MR 1476981 ]

Jeffrey F. Brock  Iteration of mapping classes on a Bers slice: examples of algebraic and geometric limits of hyperbolic $3$manifolds [ MR 1476982 ]

C. Cao, F. W. Gehring and G. J. Martin  Lattice constants and a lemma of Zagier [ MR 1476983 ]

Yungyen Chiang  The quasiFuchsian space of fourpunctured spheres [ MR 1476984 ]

Jozef Dodziuk and Varghese Mathai  Approximating $L^2$ invariants of amenable covering spaces: a heat kernel approach [ MR 1476985 ]

Tomasz Dubejko  Random walks on circle packings [ MR 1476986 ]

Clifford J. Earle  Some maximal holomorphic motions [ MR 1476987 ]

Clifford J. Earle, Frederick P. Gardiner and Nikola Lakic  Vector fields for holomorphic motions of closed sets [ MR 1476988 ]

H. M. Farkas and I. Kra  Theta constant identities with applications to combinatorial number theory [ MR 1476989 ]

Daniel M. Gallo  The topology of real projective structures [ MR 1476990 ]

Jane Gilman  A discreteness condition for subgroups of ${\rm PSL}(2,{\bf C})$ [ MR 1476991 ]

Víctor GonzálezAguilera and Rubí E. Rodríguez  On principally polarized abelian varieties and Riemann surfaces associated to prisms and pyramids [ MR 1476992 ]

A. Hinkkanen  Schur products of certain polynomials [ MR 1476993 ]

Yuri E. Hohlov and Dmitry Y. Kleinbock  Inverse problems for fluid flows with a moving boundary [ MR 1476994 ]

Yunping Jiang  On rigidity of onedimensional maps [ MR 1476995 ]

Y. Katznelson and D. S. Ornstein  Twist maps and AubryMather sets [ MR 1476996 ]

Linda Keen and Caroline Series  How to bend pairs of punctured tori [ MR 1476997 ]

I. Kra and B. Maskit  Lipman Bers, complex analyst [ MR 1476998 ]

Nikola Lakic  Strebel points [ MR 1476999 ]

Bernard Maskit  Remarks on $m$symmetric Riemann surfaces [ MR 1477000 ]

G. D. Mostow  Quasiconformal mappings of CarnotCaratheodory spaces [ MR 1477001 ]

Louis Nirenberg  Lipman Bers and partial differential equations [ MR 1477002 ]

David J. Pinchbeck  Irrational rotations [ MR 1477003 ]

Uri Srebro and Eduard Yakubov  $\mu $homeomorphisms [ MR 1477004 ]


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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 AhlforsBers mathematical tradition, broadly interpreted. Ahlfors died a year after the first colloquium; future colloquia in this series will be called The AhlforsBers 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 farreaching Bers' influence has been. The topics represented in the book include Teichmüller 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.
Features:
 Twentyseven very highlevel papers on related topics
 Open problems
 Expository articles
Graduate students and research mathematicians interested in functions of a complex variable, and related areas of mathematics.

Articles

William Abikoff and Taiping Ye  Computing the DouadyEarle extension [ MR 1476978 ]

Ara Basmajian  Selected problems in Kleinian groups and hyperbolic geometry [ MR 1476979 ]

Christopher J. Bishop and Peter W. Jones  The law of the iterated logarithm for Kleinian groups [ MR 1476980 ]

Indranil Biswas and Subhashis Nag  WeilPetersson geometry and determinant bundles on inductive limits of moduli spaces [ MR 1476981 ]

Jeffrey F. Brock  Iteration of mapping classes on a Bers slice: examples of algebraic and geometric limits of hyperbolic $3$manifolds [ MR 1476982 ]

C. Cao, F. W. Gehring and G. J. Martin  Lattice constants and a lemma of Zagier [ MR 1476983 ]

Yungyen Chiang  The quasiFuchsian space of fourpunctured spheres [ MR 1476984 ]

Jozef Dodziuk and Varghese Mathai  Approximating $L^2$ invariants of amenable covering spaces: a heat kernel approach [ MR 1476985 ]

Tomasz Dubejko  Random walks on circle packings [ MR 1476986 ]

Clifford J. Earle  Some maximal holomorphic motions [ MR 1476987 ]

Clifford J. Earle, Frederick P. Gardiner and Nikola Lakic  Vector fields for holomorphic motions of closed sets [ MR 1476988 ]

H. M. Farkas and I. Kra  Theta constant identities with applications to combinatorial number theory [ MR 1476989 ]

Daniel M. Gallo  The topology of real projective structures [ MR 1476990 ]

Jane Gilman  A discreteness condition for subgroups of ${\rm PSL}(2,{\bf C})$ [ MR 1476991 ]

Víctor GonzálezAguilera and Rubí E. Rodríguez  On principally polarized abelian varieties and Riemann surfaces associated to prisms and pyramids [ MR 1476992 ]

A. Hinkkanen  Schur products of certain polynomials [ MR 1476993 ]

Yuri E. Hohlov and Dmitry Y. Kleinbock  Inverse problems for fluid flows with a moving boundary [ MR 1476994 ]

Yunping Jiang  On rigidity of onedimensional maps [ MR 1476995 ]

Y. Katznelson and D. S. Ornstein  Twist maps and AubryMather sets [ MR 1476996 ]

Linda Keen and Caroline Series  How to bend pairs of punctured tori [ MR 1476997 ]

I. Kra and B. Maskit  Lipman Bers, complex analyst [ MR 1476998 ]

Nikola Lakic  Strebel points [ MR 1476999 ]

Bernard Maskit  Remarks on $m$symmetric Riemann surfaces [ MR 1477000 ]

G. D. Mostow  Quasiconformal mappings of CarnotCaratheodory spaces [ MR 1477001 ]

Louis Nirenberg  Lipman Bers and partial differential equations [ MR 1477002 ]

David J. Pinchbeck  Irrational rotations [ MR 1477003 ]

Uri Srebro and Eduard Yakubov  $\mu $homeomorphisms [ MR 1477004 ]