阿尔伯托·考尔德伦1920—1998

Calderón's work ranged over a wide variety of topics: from singular integral operators to partial differential equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory to inverse problems in electrical prospection. Calderón's work has also had a powerful impact on practical applications including signal processing, geophysics, and tomography.

Early life and education

Alberto Pedro Calderón was born on September 14, 1920, in Mendoza, Argentina, to Don Pedro Calderón, a physician (urologist), and Haydée. He had several siblings, including a younger brother, Calixto Pedro Calderón, also a mathematician. His father encouraged his mathematical studies. After his mother's unexpected death when he was twelve, he spent two years at the Montana Knabeninstitut, a boys' boarding school near Zürich in Switzerland, where he was mentored by Save Bercovici, who interested him in mathematics. He then completed his high school studies in Mendoza.

Persuaded by his father that he could not make a living as a mathematician, he entered the University of Buenos Aires, where he studied engineering. After graduating in civil engineering in 1947, he got a job in the research laboratory of the geophysical division of the state-owned oil company, the YPF (Yacimientos Petrolíferos Fiscales).

Research

While still working at YPF, Calderón became acquainted with the mathematicians at the University of Buenos Aires: Julio Rey Pastor, the first professor in the Institute of Mathematics, his assistant Alberto González Domínguez (who became his mentor and friend), Luis Santaló and Manuel Balanzat. At the YPF Lab Calderón studied the possibility of determining the conductivity of a body by making electrical measurements at the boundary; he did not publish his results until 1980, in his short Brazilian paper. see also On an inverse boundary value problem and the Commentary by Gunther Uhlmann. It pioneered a new area of mathematical research in inverse problems.

Calderón then took up a post at the University of Buenos Aires. Antoni Zygmund of the University of Chicago, arrived there in 1948 at the invitation of Alberto González Domínguez and Calderón was assigned as his assistant. Zygmund invited Calderón to work with him, and in 1949 Calderón arrived in Chicago with a Rockefeller Fellowship. He was encouraged by Marshall Stone to obtain a doctorate, and with three recently published papers as dissertation, Calderón obtained his PhD in mathematics under Zygmund's supervision in 1950.

The collaboration reached fruition in the Calderón-Zygmund theory of singular integrals, and lasted more than three decades.

Career

In his academic career, Calderón taught at many different universities, but primarily at the University of Chicago and the University of Buenos Aires. Calderón together with his mentor and collaborator Zygmund, maintained close ties with Argentina and Spain, and through their doctoral students and their visits, strongly influenced the development of mathematics in these countries.

• 1947 - 1950 Rockefeller Foundation Fellow, University of Chicago
• 1950 - 1953 Visiting Associate Professor, Ohio State University, Columbus, Ohio
• 1953 - 1955 Member, Institute for Advanced Study, Princeton, New Jersey
• 1955 - 1959 Associate Professor, Massachusetts Institute of Technology
• 1959 - 1968 Professor, University of Chicago
• 1968 - 1972, Louis Block Professor of Mathematics, University of Chicago
• 1972 - 1975 Professor, Massachusetts Institute of Technology
• 1975 - 1985, University Professor of Mathematics, University of Chicago
• 1975 - death, Honorary Professor, University of Buenos Aires

He was also visiting professor at universities including the University of Buenos Aires, Cornell University, Stanford University, National University of Bogotá, Colombia, Collège de France, Paris, University of Paris (Sorbonne), Autónoma and Complutense Universities, Madrid, University of Rome and Göttingen University.

Awards and honors

Calderón was recognized internationally for his outstanding contributions to Mathematics as attested to by his numerous prizes and membership in various academies. He gave many invited addresses to universities and learned societies. In particular he addressed the International Congress of Mathematicians: a) as invited lecturer in Moscow in 1966 and b) as plenary lecturer in Helsinki in 1978. The Instituto Argentino de Matemática (I.A.M.), based in Buenos Aires, a prime research center of the National Research Council of Argentina (CONICET), now honors Alberto Calderón by bearing his name: Instituto Argentino de Matemática Alberto Calderón. In 2007, the Inverse Problems International Association (IPIA) instituted the Calderón Prize, named in honor of Alberto P. Calderón, and awarded to a "researcher who has made distinguished contributions to the field of inverse problems broadly defined".

Academies

1958 Member, American Academy of Arts and Sciences, Boston, Massachusetts

1959 Correspondent Member, National Academy of Exact, Physical and Natural Sciences, Buenos Aires, Argentina

1968 Member, National Academy of Sciences of the U.S.A.

1970 Correspondent Member, Royal Academy of Sciences, Madrid, Spain

1983 Member, Latin American Academy of Sciences, Caracas, Venezuela

Selected papers

Calderón, A. P.; Zygmund, A. (1952), "On the existence of certain singular integrals", Acta Mathematica, 88 (1): 85–139, doi:10.1007/BF02392130, ISSN 0001-5962, MR 0052553, Zbl 0047.10201. This is one of the key papers on singular integral operators.

Calderón, A. P. (1958). "Uniqueness in the Cauchy Problem for Partial Differential Equations". American Journal of Mathematics. 80 (1): 16–36. doi:10.2307/2372819. JSTOR 2372819. S2CID 123717719.

Calderón, A. P. (1963): "Boundary value problems for elliptic equations", Outlines for the Joint Soviet - American Symposium on Partial Differential Equations, Novosibirsk, pp. 303–304.

Calderón, A. P. (1977). "Cauchy integrals on Lipschitz curves and related operators". Proceedings of the National Academy of Sciences of the United States of America. 74 (4): 1324–1327. Bibcode:1977PNAS...74.1324C. doi:10.1073/pnas.74.4.1324. PMC 430741. PMID 16578748.

Calderón, A. P. (1980): "Commutators, Singular Integrals on Lipschitz curves and Applications", Proc. Internat. Congress of Math. 1978, Helsinki, pp. 85–96.

Calderón, A. P. (1964). "Intermediate spaces and interpolation, the complex Method" (PDF). Studia Mathematica. 24 (2): 113–190. doi:10.4064/sm-24-2-113-190.