Alberto Calderón

Alberto Pedro Calderón (September 14, 1920 – April 16, 1998) was an Argentine-American mathematician. His name is associated with the University of Buenos Aires, but first and foremost with the University of Chicago, where Calderón and his mentor, the analyst Antoni Zygmund, developed the theory of singular integral operators.

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. 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. 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. 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. see also the Commentary by Charles Fefferman and Elias M. Stein, (see also the Commentary by Donald L. Burkholder, ) 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.

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, 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, awarded by the Wolf Foundation, Jerusalem, Israel 1989 Steele Prize, awarded by the American Mathematical Society 1991 National Medal of Science, 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.