Eugenio Calabi
Eugenio Calabi | |
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Xiu-Xiong Chen |
Eugenio Calabi (May 11, 1923 – September 25, 2023) was an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications.
Early life and education
Calabi was born in Milan, Italy on May 11, 1923, into a Jewish family.[1] His sister was the journalist Tullia Zevi Calabi. In 1938, the family left Italy because of the racial laws, and in 1939 arrived in the United States.[2][3]
In the fall of 1939, aged only 16, Calabi enrolled at the Massachusetts Institute of Technology, studying chemical engineering. His studies were interrupted when he was drafted in the US military in 1943 and served during World War II. Upon his discharge in 1946, Calabi was able to finish his bachelor's degree under the G.I. Bill, and was a Putnam Fellow.[3][4] He received a master's degree in mathematics from the University of Illinois Urbana-Champaign in 1947 and his PhD in mathematics from Princeton University in 1950. His doctoral dissertation, titled "Isometric complex analytic imbedding of Kähler manifolds", was done under the supervision of Salomon Bochner.[5]
Academic career
From 1951 to 1955 he was an assistant professor at Louisiana State University, and he moved to the University of Minnesota in 1955, where he became a full professor in 1960. In 1964, Calabi joined the mathematics faculty at the University of Pennsylvania. Following the retirement of Hans Rademacher, he was appointed to the Thomas A. Scott Professorship of Mathematics at the University of Pennsylvania in 1968. In 1994, Calabi assumed emeritus status, and in 2014 the university awarded him an honorary doctorate of science.[6][7][8]
In 1982, Calabi was elected to the National Academy of Sciences.[9] He won the Leroy P. Steele Prize from the American Mathematical Society in 1991, where his "fundamental work on global differential geometry, especially complex differential geometry" was cited as having "profoundly changed the landscape of the field".[8] In 2012, he became a fellow of the American Mathematical Society.[10] In 2021, he was awarded Commander of the Order of Merit of the Italian Republic.[11][7]
Calabi married Giuliana Segre in 1952, with whom he had a son and a daughter. He turned 100 on May 11, 2023, and died on September 25.[7][12]
Research
Calabi made a number of contributions to the field of
Kähler geometry
At the 1954 International Congress of Mathematicians, Calabi announced a theorem on how the Ricci curvature of a Kähler metric could be prescribed.[C54] He later found that his proof, via the method of continuity, was flawed, and the result became known as the Calabi conjecture. In 1957, Calabi published a paper in which the conjecture was stated as a proposition, but with an openly incomplete proof.[C57] He gave a complete proof that any solution of the problem must be uniquely defined, but was only able to reduce the problem of existence to the problem of establishing a priori estimates for certain partial differential equations. In the 1970s, Shing-Tung Yau began working on the Calabi conjecture, initially attempting to disprove it. After several years of work, he found a proof of the conjecture, and was able to establish several striking algebro-geometric consequences of its validity. As a particular case of the conjecture, Kähler metrics with zero Ricci curvature are established on a number of complex manifolds; these are now known as Calabi–Yau metrics. They have become significant in string theory research since the 1980s.[14][15][16]
In 1982, Calabi introduced a
A well-known construction of Calabi's puts complete Kähler metrics on the total spaces of hermitian vector bundles whose curvature is bounded below.[C79] In the case that the base is a complete Kähler–Einstein manifold and the vector bundle has rank one and constant curvature, one obtains a complete Kähler–Einstein metric on the total space. In the case of the cotangent bundle of a complex space form, one obtains a hyperkähler metric. The Eguchi–Hanson space is a special case of Calabi's construction.[14]
Geometric analysis
Calabi found the Laplacian comparison theorem in
In parallel to the classical
Later, Calabi considered the problem of
Differential geometry
Calabi and
Inspired by recent work of
Calabi and Lawrence Markus considered the problem of
Work of
Later, Calabi studied the two-dimensional
Publications
C53. | Calabi, Eugenio (1953). "Isometric imbedding of complex manifolds".
Zbl 0051.13103 . |
CE53. | Calabi, Eugenio;
Zbl 0051.40304 . |
C54. | Calabi, E. (1954). "The space of Kähler metrics" (PDF). In Gerretsen, Johan C. H.;
North-Holland Publishing Co. pp. 206–207. |
C57. | Calabi, Eugenio (1957). "On Kähler manifolds with vanishing canonical class". In
Zbl 0080.15002 . |
C58a. | Calabi, E. (1958). "An extension of E. Hopf's maximum principle with an application to Riemannian geometry". )
|
C58b. | Calabi, Eugenio (1958). "Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens".
Zbl 0113.30104 . |
CV60. | Calabi, Eugenio;
Zbl 0100.36002 . |
CM62. | Calabi, E.; Markus, L. (1962). "Relativistic space forms".
Zbl 0101.21804 . |
C67. | Calabi, Eugenio (1967). "Minimal immersions of surfaces in Euclidean spheres".
Zbl 0171.20504 . |
C70. | Calabi, Eugenio (1970). "Examples of Bernstein problems for some nonlinear equations". In
Zbl 0211.12801 . |
C72. | Calabi, Eugenio (1972). Complete affine hyperspheres. I. Convegno di Geometria Differenziale (24–28 Maggio 1971); Convegno di Analisi Numerica (10–13 Gennaio 1972). Istituto Nazionale di Alta Matematica, Rome. Symposia Mathematica. Vol. X. London:
Zbl 0252.53008 . |
C79. | Calabi, E. (1979). "Métriques kählériennes et fibrés holomorphes". Annales Scientifiques de l'École Normale Supérieure. Quatrième Série. 12 (2): 269–294.
Zbl 0431.53056 . |
C82. | Calabi, Eugenio (1982). "Extremal Kähler metrics". In
Zbl 0487.53057 . |
C85. | Calabi, Eugenio (1985). "Extremal Kähler Metrics II". In Chavel, I.; Farkas, H. M. (eds.). Differential Geometry and Complex Analysis. Berlin:
Zbl 0574.58006 . |
CC02. | Calabi, E.;
Zbl 1067.58010 . |
Calabi's collected works were published in 2021:
- Calabi, Eugenio (2021). Zbl 1457.32001.
References
- ^ American Men and Women of Science, Thomson Gale 2004
- ^ Calabi, Eugenio (January 24, 2012). "A Tribute to the Italian-Jewish Journalist Tullia Calabi Zevi". Penn Arts & Sciences, Italian Studies.
- ^ a b Arntzenius, Linda (January 21, 2016). "Oral History Project: Eugenio Calabi Interviewed by Linda Arntzenius". Shelby White and Leon Levy Archives Center, Institute for Advanced Study.
- ^ "Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved December 10, 2021.
- ^ Eugenio Calabi at the Mathematics Genealogy Project
- ^ "Penn's 2014 Commencement Speaker and Honorary Degree Recipients". University of Pennsylvania Almanac. Vol. 60, no. 23. February 18, 2014.
- ^ a b c Miles, Gary (September 28, 2023). "Eugenio Calabi, child prodigy, renowned mathematician, and professor emeritus at Penn, has died at 100". The Philadelphia Inquirer. Retrieved September 29, 2023.
- ^ a b "1991 Steele Prizes Awarded in Orono" (PDF). Notices of the American Mathematical Society. 38 (8). October 1991.
- ^ "Eugenio Calabi". National Academy of Sciences. Retrieved October 1, 2023.
- ^ List of Fellows of the American Mathematical Society, retrieved November 10, 2012.
- ^ "Official Gazette of the Italian Republic, 2022 March 17".
- ^ "Tribute to Eugenio Calabi". Institut des Hautes Études Scientifiques. September 27, 2023.
- ^ Calabi 2021.
- ^ Zbl 0613.53001.
- Zbl 1123.81001.
- Zbl 1435.32001.
- Zbl 0312.53031.
- Zbl 1417.53001.
- ^ Zbl 0834.53002.
- Zbl 0623.53002.
- Zbl 0444.32004.
- ^ Zbl 1246.53001.
- Zbl 1380.53001.
- ^ Calabi & Markus 1962, MR review.
- Zbl 0265.53054.
- Zbl 1216.53003..
- Zbl 1055.53049.
- Zbl 0498.53046.
- Zbl 0515.58011.
Further reading
- Zbl 0926.53001.
- Zbl 0911.53002.
- doi:10.4171/MAG/144.
- Nadis, Steve (October 16, 2023). "The mathematician who sculpted the shape of space". Quanta Magazine.