Alberto Pedro Calderón (September 14, 1920 – April 16, 1998) was an Argentine mathematician. His name is associated with the
University of Buenos Aires, but first and foremost with the
University of Chicago
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
, where Calderón and his mentor, the analyst
Antoni Zygmund, developed the theory of
singular integral operators.
This created the "
Chicago School of (hard) Analysis" (sometimes simply known as the "Calderón-Zygmund School").
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
Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behav ...
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
Argentina, officially the Argentine Republic, is a country in the southern half of South America. It covers an area of , making it the List of South American countries by area, second-largest country in South America after Brazil, the fourt ...
, 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
Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...
in
Switzerland
Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. 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
Civil engineering is a regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads ...
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 als
On an inverse boundary value problemand the Commentary by
Gunther Uhlmann.
[(2008) SELECTED PAPERS OF ALBERTO P. CALDERON WITH COMMENTARY, Alexandra Bellow, Carlos E. Kenig and Paul Malliavin, Editors, ''Amer. Math. Soc., Providence, Rhode Island'', CWORKS/21.] It pioneered a new area of mathematical research in
inverse problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, sound source reconstruction, source reconstruction in ac ...
s.
Calderón then took up a post at the
University of Buenos Aires.
Antoni Zygmund of the
University of Chicago
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
, 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. The memoir of 1952 was influential for the
Chicago School of hard analysis. The
Calderón-Zygmund decomposition lemma, invented to prove the
weak-type continuity of singular integrals of integrable functions, became a standard tool in analysis and probability theory. The Calderón-Zygmund Seminar at the University of Chicago ran for decades.
Calderón contributed to the theory of differential equations, with his proof of uniqueness in the
Cauchy problem using algebras of singular integral operators, his reduction of elliptic boundary value problems to singular integral equations on the boundary (the "method of the Calderón projector"), and the role played by algebras of singular integrals, through the work of Calderón's student R. Seeley, in the initial proof of the
Atiyah-Singer index theorem, see also the Commentary by Paul Malliavin.
The development of
pseudo-differential operators by Kohn-Nirenberg and Hörmander also owed much to Calderón and his collaborators, R. Vaillancourt and J. Alvarez-Alonso.
Also, Calderón insisted that the focus should be on algebras of singular integral operators with non-smooth kernels to solve actual problems arising in physics and engineering, where lack of smoothness is a natural feature. It led to what is now known as the "Calderón program", with major parts: Calderón's study of the Cauchy integral on
Lipschitz curves, and his proof of the ''boundedness of the "first commutator"''. These papers stimulated research by other mathematicians in the following decades; see also the later paper by the Calderón brothers
and the Commentary by Y. Meyer.
Work by Calderón in interpolation theory opened up a new area of research, see also the Commentary by Charles Fefferman and Elias M. Stein,
and in
ergodic theory
Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behav ...
, his basic paper (see also the Commentary by Donald L. Burkholder,
and
[(1999) HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS, ''Essays in Honor of Alberto P. Calderón'', Michael Christ, Carlos E. Kenig and Cora Sadosky, Editors, ''The University of Chicago Press'', "Transference Principles in Ergodic Theory" by Alexandra Bellow, pp. 27–39]) formulated a transference principle that reduced the proof of
maximal inequalities for abstract dynamical systems to the case of the dynamical system on the integers, on the reals or, more generally, on the acting group.
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
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
* 1950 - 1953 Visiting Associate Professor,
Ohio State University
The Ohio State University (Ohio State or OSU) is a public university, public Land-grant university, land-grant research university in Columbus, Ohio, United States. A member of the University System of Ohio, it was founded in 1870. It is one ...
, Columbus, Ohio
* 1953 - 1955 Member,
Institute for Advanced Study
The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
, Princeton, New Jersey
* 1955 - 1959 Associate Professor,
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
* 1959 - 1968 Professor,
University of Chicago
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
* 1968 - 1972, ''Louis Block Professor of Mathematics'',
University of Chicago
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
* 1972 - 1975 Professor,
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
* 1975 - 1985, ''University Professor of Mathematics'',
University of Chicago
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
* 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
* 1984 Member, National Academy of Exact, Physical and Natural Sciences, Buenos Aires, Argentina
* 1984 Foreign Associate, Institut de France, Paris, France
* 1984 Member, Third World Academy of Sciences, Trieste, Italy
Prizes
* 1969
Latin American Prize in Mathematics, awarded by IPCLAR (Instituto para la Promoción de las Ciencias, Letras y Realizaciones), Santa Fe, Argentina
* 1979
Bôcher Memorial Prize
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five yea ...
, awarded by the American Mathematical Society
* 1983
Konex Award (Science and Technology), Buenos Aires, Argentina
* 1989
Premio de Consagración Nacional, Buenos Aires, Argentina
* 1989
Wolf Prize
The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...
, awarded by the Wolf Foundation, Jerusalem, Israel
* 1989
Steele Prize, awarded by the American Mathematical Society
* 1991
National Medal of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral science, behavior ...
, Washington D.C., U.S.A.
Honorary degrees
* 1969 ''Doctor Honoris Causa'', University of Buenos Aires, Argentina
* 1989 ''Doctor of Science, Honoris Causa'', Technion, Haifa, Israel
* 1995 ''Doctor of Science, Honoris Causa'', Ohio State University, Columbus, Ohio
* 1997 ''Doctor Honoris Causa'', Universidad Autónoma de Madrid, Spain
Selected papers
# . This is one of the key papers on
singular integral operators.
#
# 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. (1980)
"Commutators, Singular Integrals on Lipschitz curves and Applications" ''Proc. Internat. Congress of Math. 1978, Helsinki'', pp. 85–96.
#
#
#
References
External links
*
*
Obituary: Alberto Calderon, University of Chicago ChronicleAlberto Pedro Calderón (1920–1998), Notices of the AMS
{{DEFAULTSORT:Calderon, Alberto
1920 births
1998 deaths
People from Mendoza, Argentina
20th-century Argentine mathematicians
University of Chicago alumni
Ohio State University faculty
Massachusetts Institute of Technology faculty
Institute for Advanced Study visiting scholars
University of Chicago faculty
National Medal of Science laureates
Members of the United States National Academy of Sciences
Wolf Prize in Mathematics laureates
Partial differential equation theorists
Argentine expatriates in the United States
University of Buenos Aires alumni