Biographical Memoirs Volume 80 (2001) / Chapter Skim
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Lipman Bers
Lipman Bers
Pages 22-43
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of Israel. He opposed nuclear armaments as if there were no coIcl war, he fought tyranny as if this struggle hacl no arms contro!
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After a brief period in Zurich, Lipa returned to the university in Riga, as a politically involvecl social democrat in an atmosphere of growing political turmoil en c! violence.
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They fleck to Paris, where their application for an American visa resultecl in not uncommon frustration. The brief interlucle in Paris proclucecl two short mathematical papers: one on Green's functions, another on integral representations of biharmonic functions, these were partly inspired by Stefan Bergman's then-influential work on kernel functions.
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Although the result belongs to the fielcl of partial clifferential equations, the methods are from complex analysis, hinting at the direction of his most important future work. QUASICONFORMAL MAPPINGS, TEICHMULLER THEORY, AND KLEINIAN GROUPS Bers's 1948 paper in the Bulletin of the American Mathematical Society, "On rings of analytic functions," created a small industry that contributed to an aigebraization of ques
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in unclerstancling the different ways one can clo complex analysis on a fixed topological surface. One of the important open problems, the mocluli problem, left to us from the nineteenth century, was to make rigorous en cl precise Bernharcit Riemann's claim that the complex analytic structure on a closecl surface with p 2 2 hancIles clepencis on 3~3 complex parameters.
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Quasiconformal mappings can also be used to study complex analytic aspects of moduTi theory. There is a deep connection between the theory of moduli and univalent functions since a very important class of such functions can be obtainea as solutions of BeTtrami equations.
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smooth functions to construct cohomology classes from a class of holomorphic functions known as cusp forms. He then neeclec!
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Its solution, publishecl in Acta Mathematica in 1978, proviclecl an alternate classification of self-maps of surfaces, showocl the intimate connections of this set of problems to mocluTi problems, en cl involvecl Riemann surfaces with simple singularities, a topic aIreacly of interest to Bers for other reasons (to construct analytically the compactification of mocluTi spaces of nonsingular curves) .~4 Bers cIaimecl that he was very lucky to be surrounclecl by ~.
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The first chapters of an autobiography are in the hands of the Bers family. MENTOR AND EXPOSITOR Lipman Bers's students were immecliately acimittecl to the extenclec!
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partial differential equations are such examples. His graduate teaching at NYU proclucecl influential sets of lecture notes on pseudoanalytic functions (1952)
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wisdom that he brought to social issues playact itself out mainly on three stages: at Columbia cluring the anti-Vietnam War protests, at the American Mathematical Society, as vice president 1963-65 and presi
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victims of McCarthyism and cold-war politics obtain acaclemic positions. In opposing the Vietnam War, Lipa felt a strong moral sympathy with the protest movement, but often triecl to temper its destructive excesses.
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I believe that only a truly even-handed approach can lead to an honest, morally convincing, and effective human rights policy. A human rights activist who hates and fears communism must also care about the human rights of Latin American leftists.
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ever the politician. continued: ~ 1- ~ ' 1"Now, if we want to do things beyond this and participate in organizing a social democratic party in America, I will gladly discuss this later." In his personal life and in advancing his social agenda, especially on human rights, Lipa was remarkably accurate in foreseeing the future.
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It was however quite fitting that the first issue of the new revisecIi9 Notices of the AMS January 1995) featured a number of articles "Remembering Lipman Bers." In the worcis of his friend Arych Dvoretsky "Like the sun in our sky, he cast a giant light."
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He was looking for an inequality that would establish an existence theorem in partial differential equations and suspected that quasiconformal mappings might provide the needed a priori estimate.
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17. Bers was the first Hardy Lecturer, an honor bestowed by the London Mathematical Society.
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is a perfect example of the role of complex analytic methods in related fields. His only paper on spaces of analytic functions k2]
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, Selected Works of Lipman Bers: Papers on Complex Analysis, American Mathematical Society, 1998.
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