eBook ISBN:  9780821878033 
Product Code:  CONM/211.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821878033 
Product Code:  CONM/211.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

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 ]