Lipman Bers | |
|---|---|
| Born | (1914-05-22)May 22, 1914 |
| Died | October 29, 1993(1993-10-29) (aged 79) New Rochelle,New York, U.S. |
| Nationality | Latvian American |
| Alma mater | University of Zurich University of Riga University of Prague (PhD) |
| Known for | Bers compactification Bers area inequality Bers slice Density theorem for Kleinian groups Measurable Riemann mapping theorem Pseudoanalytic function Simultaneous uniformization theorem Universal Teichmüller space |
| Children | Victor Bers (son) |
| Awards | Leroy P. Steele Prize (1975) Guggenheim Fellowship (1975) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | New York University Columbia University Brown University Syracuse University |
| Doctoral advisor | Charles Loewner |
| Doctoral students | |
Lipman Bers (Latvian:Lipmans Berss; May 22, 1914 – October 29, 1993) was a Latvian-Americanmathematician, born inRiga, who created the theory ofpseudoanalytic functions and worked onRiemann surfaces andKleinian groups. He was also known for his work in human rights activism.[1][2]
Bers was born in Riga, then under the rule of the Russian Czars, and spent several years as a child inSaint Petersburg; his family returned to Riga in approximately 1919, by which time it was part of independentLatvia. In Riga, his mother was the principal of a Jewish elementary school, and his father became the principal of a Jewish high school, both of which Bers attended, with an interlude inBerlin while his mother, by then separated from his father, attended theBerlin Psychoanalytic Institute. After high school, Bers studied at theUniversity of Zurich for a year, but had to return to Riga again because of the difficulty of transferring money from Latvia in the international financial crisis of the time. He continued his studies at theUniversity of Riga, where he became active in socialist politics, including giving political speeches and working for an underground newspaper. In the aftermath of the Latvian coup in 1934 by right-wing leaderKārlis Ulmanis, Bers was targeted for arrest but fled the country, first to Estonia and then to Czechoslovakia.[1][3][4]
Bers received his Ph.D. in 1938 from theUniversity of Prague.[5] He had begun his studies in Prague withRudolf Carnap, but when Carnap moved to the US he switched toCharles Loewner, who would eventually become his thesis advisor. In Prague, he lived with an aunt, and married his wife Mary (née Kagan) whom he had met in elementary school and who had followed him from Riga. Having applied for postdoctoral studies in Paris, he was given a visa to go to France soon after theMunich Agreement, by which Nazi Germany annexed theSudetenland. He and his wife Mary had a daughter in Paris. They were unable to obtain a visa there to emigrate to the US, as the Latvian quota had filled, so they escaped to the south of France ten days before the fall of Paris, and eventually obtained an emergency US visa in Marseilles, one of a group of 10,000 visas set aside for political refugees byEleanor Roosevelt. The Bers family rejoined Bers' mother, who had by then moved toNew York City and become a psychoanalyst, married to thespian Beno Tumarin. At this time, Bers worked for theYIVO Yiddish research agency.[1][2][3][4]
Bers spent World War II teaching mathematics as a research associate atBrown University, where he was joined by Loewner. After the war, Bers found an assistant professorship atSyracuse University (1945–1951), before moving toNew York University (1951–1964) and thenColumbia University (1964–1982), where he became the Davies Professor of Mathematics,[3][4] and where he chaired the mathematics department from 1972 to 1975.[6] His move to NYU coincided with a move of his family toNew Rochelle, New York, where he joined a small community of émigré mathematicians.[6] He was a visiting scholar at theInstitute for Advanced Study in 1949–51.[7] He was a Vice-President (1963–65) and a President (1975–77) of theAmerican Mathematical Society, chaired the Division of Mathematical Sciences of theUnited States National Research Council from 1969 to 1971, chaired the U.S. National Committee on Mathematics from 1977 to 1981, and chaired the Mathematics Section of theNational Academy of Sciences from 1967 to 1970.[4][8]
Late in his life, Bers suffered fromParkinson's disease andstrokes. He died on October 29, 1993.[4]
Bers' doctoral work was on the subject ofpotential theory. While in Paris, he worked onGreen's function and on integral representations. After first moving to the US, while working for YIVO, he researched Yiddish mathematics textbooks rather than pure mathematics.[6]
At Brown, he began working on problems offluid dynamics, and in particular on the two-dimensional subsonic flows associated with cross-sections ofairfoils. At this time, he began his work withAbe Gelbart on what would eventually develop into the theory ofpseudoanalytic functions. Through the 1940s and 1950s he continued to develop this theory, and to use it to study the planarelliptic partial differential equations associated with subsonic flows. Another of his major results in this time concerned the singularities of the partial differential equations definingminimal surfaces. Bers proved an extension ofRiemann's theorem on removable singularities, showing that any isolated singularity of a pencil of minimal surfaces can be removed; he spoke on this result at the 1950International Congress of Mathematicians and published it inAnnals of Mathematics.[6]
Later, beginning with his visit to the Institute for Advanced Study, Bers "begana ten-year odyssey that took him from pseudoanalytic functions and elliptic equations toquasiconformal mappings,Teichmüller theory, andKleinian groups".[6] WithLars Ahlfors, he solved the "moduli problem", of finding aholomorphic parameterization of theTeichmüller space, each point of which represents acompactRiemann surface of a given genus. During this period he also coined the popular phrasing of a question on eigenvalues of planar domains, "Can one hear the shape of a drum?", used as an article title byMark Kac in 1966 and finally answered negatively in 1992 by anacademic descendant of Bers. In the late 1950s, by way of adding a coda to his earlier work, Bers wrote several major retrospectives of flows, pseudoanalytic functions,fixed point methods, Riemann surface theory prior to his work on moduli, and the theory ofseveral complex variables. In 1958, he presented his work on Riemann surfaces in a second talk at the International Congress of Mathematicians.[6]
Bers' work on the parameterization of Teichmüller space led him in the 1960s to consider the boundary of the parameterized space, whose points corresponded to new types ofKleinian groups, eventually to be calledsingly-degenerate Kleinian groups. He appliedEichler cohomology, previously developed for applications in number theory and the theory ofLie groups, to Kleinian groups. He proved theBers area inequality, an area bound for hyperbolic surfaces that became a two-dimensional precursor toWilliam Thurston's work ongeometrization of 3-manifolds and 3-manifold volume, and in this period Bers himself also studied the continuous symmetries of hyperbolic 3-space.[6]
Quasi-Fuchsian groups may be mapped to a pair of Riemann surfaces by taking the quotient by the group of one of the two connected components of the complement of the group's limit set; fixing the image of one of these two maps leads to a subset of the space of Kleinian groups called aBers slice. In 1970, Bers conjectured that the singly degenerate Kleinian surface groups can be found on the boundary of a Bers slice; this statement, known as theBers density conjecture, was finally proven by Namazi, Souto, and Ohshika in 2010 and 2011.[9][10] TheBers compactification of Teichmüller space also dates to this period.
Over the course of his career, Bersadvised approximately 50 doctoral students,[11] among themEnrico Arbarello,Irwin Kra,Linda Keen,Murray H. Protter, andLesley Sibner.[5] Approximately a third of Bers' doctoral students were women, a high proportion for mathematics.[8][12] Having felt neglected by his own advisor,[3] Bers met regularly for meals with his students and former students,[6] maintained a keen interest in their personal lives as well as their professional accomplishments,[12] and kept up a friendly competition withLars Ahlfors over who could bring to larger number of academic descendants to mathematical gatherings.[2]
As a small child with his mother in Saint Petersburg, Bers had cheered the Russian Revolution and the rise of theSoviet Union, but by the late 1930s he had become disillusioned with communism after the assassination ofSergey Kirov andStalin's ensuingpurges.[3] His son,Victor Bers, later said that "His experiences in Europe motivated his activism in the human rights movement,"[4] and Bers himself attributed his interest in human rights to the legacy ofMenshevik leaderJulius Martov.[3] He founded the Committee on Human Rights of theNational Academy of Sciences,[4][13] and beginning in the 1970s worked to allow the emigration of dissident Soviet mathematicians including Yuri Shikhanovich,Leonid Plyushch,Valentin Turchin, andDavid and Gregory Chudnovsky.[4] Within the U.S., he also opposed the American involvement in theVietnam War and southeast Asia,[2][6] and the maintenance of the U.S. nuclear arsenal during theCold War.[2]
In 1961, Bers was elected a Fellow of theAmerican Academy of Arts and Sciences,[14] and in 1965 he became a Fellow of theAmerican Association for the Advancement of Science.[6] He joined theNational Academy of Sciences in 1964.[6] He was a member of theFinnish Academy of Sciences, and theAmerican Philosophical Society. He received theAMSLeroy P. Steele Prize for mathematical exposition in 1975 for his paper "Uniformization, moduli, and Kleinian groups". In 1986, theNew York Academy of Sciences gave him their Human Rights Award.[4] In the early 1980s, theAssociation for Women in Mathematics held a symposium to honor Bers' accomplishments in mentoring women mathematicians.[3]
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