Lipman Bers

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Lipman Bers
Born(1914-05-22)May 22, 1914
PhD)
Known forBers compactification
Bers area inequality
Bers slice
Density theorem for Kleinian groups
Measurable Riemann mapping theorem
Pseudoanalytic function
Simultaneous uniformization theorem
Universal Teichmüller space
ChildrenVictor Bers (son)
AwardsLeroy P. Steele Prize (1975)
Guggenheim Fellowship (1975)
Scientific career
FieldsMathematics
InstitutionsNew York University
Columbia University
Brown University
Syracuse University
Doctoral advisorCharles Loewner
Doctoral students

Lipman Bers (Latvian: Lipmans Berss; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism.[1][2]

Biography

Bers was born in Riga, then under the rule of the Russian Czars, and spent several years as a child in

University 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 leader Kārlis 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 the

University of Prague.[5] He had begun his studies in Prague with Rudolf Carnap, but when Carnap moved to the US he switched to Charles 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 the Munich Agreement, by which Nazi Germany annexed part of Czechoslovakia. 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 by Eleanor Roosevelt. The Bers family rejoined Bers' mother, who had by then moved to New York City and become a psychoanalyst, married to thespian Beno Tumarin. At this time, Bers worked for the YIVO Yiddish research agency.[1][2][3][4]

Bers spent World War II teaching mathematics as a research associate at

United 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 the National Academy of Sciences from 1967 to 1970.[4][8]

Late in his life, Bers suffered from Parkinson's disease and strokes. He died on October 29, 1993.[4]

Mathematical research

Bers' doctoral work was on the subject of potential theory. While in Paris, he worked on Green'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 of fluid dynamics, and in particular on the two-dimensional subsonic flows associated with cross-sections of airfoils. At this time, he began his work with Abe Gelbart on what would eventually develop into the theory of pseudoanalytic functions. Through the 1940s and 1950s he continued to develop this theory, and to use it to study the planar elliptic partial differential equations associated with subsonic flows. Another of his major results in this time concerned the singularities of the partial differential equations defining minimal surfaces. Bers proved an extension of Riemann'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 1950 International Congress of Mathematicians and published it in Annals of Mathematics.[6]

Later, beginning with his visit to the Institute for Advanced Study, Bers "began a ten-year odyssey that took him from pseudoanalytic functions and elliptic equations to

Teichmüller theory
, and
several 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 of

Bers area inequality, an area bound for hyperbolic surfaces that became a two-dimensional precursor to William Thurston's work on geometrization of 3-manifolds and 3-manifold volume, and in this period Bers himself also studied the continuous symmetries of hyperbolic 3-space.[6]

Bers compactification
of Teichmüller space also dates to this period.

Advising

Over the course of his career, Bers advised approximately 50 doctoral students,[11] among them Enrico Arbarello, Irwin Kra, Linda Keen, Murray H. Protter, and Lesley 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 with Lars Ahlfors over who could bring to larger number of academic descendants to mathematical gatherings.[2]

Human rights activism

As a small child with his mother in Saint Petersburg, Bers had cheered the Russian Revolution and the rise of the

Menshevik leader Julius Martov.[3] He founded the Committee on Human Rights of the National 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, and David and Gregory Chudnovsky.[4] Within the U.S., he also opposed the American involvement in the Vietnam War and southeast Asia,[2][6] and the maintenance of the U.S. nuclear arsenal during the Cold War.[2]

Awards and honors

In 1961, Bers was elected a Fellow of the American Academy of Arts and Sciences,[14] and in 1965 he became a Fellow of the American Association for the Advancement of Science.[6] He joined the National Academy of Sciences in 1964.[6] He was a member of the Finnish Academy of Sciences, and the American Philosophical Society. He received the AMS Leroy P. Steele Prize for mathematical exposition in 1975 for his paper "Uniformization, moduli, and Kleinian groups". In 1986, the New York Academy of Sciences gave him their Human Rights Award.[4] In the early 1980s, the Association for Women in Mathematics held a symposium to honor Bers' accomplishments in mentoring women mathematicians.[3]

Publications

Books

  • Bers, Lipman (1953), Theory of pseudo-analytic functions, Institute for Mathematics and Mechanics, New York University, New York,
    MR 0057347
  • Bers, Lipman (1958), Mathematical aspects of subsonic and transonic gas dynamics, New York: John Wiley & Sons[15]
  • Bers, Lipman (1976), Calculus, Holt, Rinehart and Winston, (in collaboration with Frank Karal)[16]
  • Bers, Lipman (1998),
    MR 1643465
  • Bers, Lipman (1998),
    MR 1643469

Selected articles

References

  1. ^ a b c O'Connor, John J.; Robertson, Edmund F., "Lipman Bers", MacTutor History of Mathematics Archive, University of St Andrews
  2. ^ a b c d e Bass, Hyman; Kra, Irwin, Lipman Bers, May 22, 1914 — October 29, 1993, Biographical Memoirs of the National Academy of Sciences, National Academies Press.
  3. ^ a b c d e f g Albers, Donald J.; Alexanderson, Gerald L.; Reid, Constance, eds. (1990), "Lipman Bers", More Mathematical People, Harcourt Brace Jovanovich, pp. 2–21.
  4. ^ a b c d e f g h i "Lipman Bers, 79, Human Rights Activist, Dies", Columbia University Record, 19 (10), November 12, 1993.
  5. ^ a b Lipman Bers at the Mathematics Genealogy Project
  6. ^
    Notices of the AMS
    , 42 (1): 8–18.
  7. ^ Community of Scholars Profile, Institute for Advanced Study, retrieved March 30, 2013.
  8. ^ a b "43. Lipman Bers (1914–1993)", AMS Presidents: A Timeline, American Mathematical Society, retrieved March 30, 2013.
  9. ^ Namazi, Hossein; Souto, Juan (2010), Non-realizability, ending laminations and the density conjecture, archived from the original on July 15, 2009.
  10. S2CID 14463721, archived from the original
    on May 25, 2014, retrieved March 31, 2013
  11. ^ The Mathematics Genealogy database lists 53, but other sources count only 48.
  12. ^
    Notices of the AMS
    , 42 (1): 22–23.
  13. Notices of the AMS
    , 42 (1): 18–22.
  14. ^ "Book of Members, 1780–2010: Chapter B" (PDF). American Academy of Arts and Sciences. Retrieved June 24, 2011.
  15. doi:10.1090/s0002-9904-1961-10602-2
    .
  16. ^ Reviewed Work: Calculus by Lipman Bers, Review by: W. H. Fleming, The American Mathematical Monthly Vol. 77, No. 2 (Feb. 1970), pp. 200-201: https://www.jstor.org/stable/2317353

External links

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