Aldo Andreotti (15 March 1924 – 21 February 1980) was an Italian mathematician who worked on
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
, on the
theory of functions of several complex variables and on
partial differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and retur ...
s. Notably he proved the
Andreotti–Frankel theorem
In mathematics, the Andreotti–Frankel theorem, introduced by , states that if V is a smooth algebraic variety, smooth, complex affine variety of complex dimension n or, more generally, if V is any Stein manifold of dimension n, then
V admits a ...
, the
Andreotti–Grauert theorem In mathematics, the Andreotti–Grauert theorem, introduced by , gives conditions for cohomology groups of coherent sheaves
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of shea ...
, the
Andreotti–Vesentini theorem
In mathematics, the Andreotti–Vesentini separation theorem, introduced by states that certain cohomology groups of coherent sheaves
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a cla ...
and introduced, jointly with
François Norguet, the
Andreotti–Norguet integral representation for functions of several complex variables.
Andreotti was a visiting scholar at the
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
in 1951 and again from 1957 through 1959.
Selected publications
Aldo Andreotti published 100 scientific works, including papers, books and lecture notes: many of them, except all his books but , are collected in his "''Selecta''" . In his "Selecta" are also included three unpublished sets of lecture notes, the first one prepared by Philippe Artzner from a course on the theory of analytic functions of several complex variables held by Andreotti during winter 1961 at the
University of Strasbourg
The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers.
The French university traces its history to the ea ...
, the second and third ones taken from two lectures held by Francesco Gherardelli at the "Seminario di Geometria" of the Scuola Normale Superiore during the years 1971–1972 and 1971–1972 respectively, on topics concerning his joint work with Andreotti: despite their nature of unpublished works, states that they have brought significant contributions to research.
[Precisely, writes:-"''Ad esse si aggiungono due opere – mai apparse in libri e riviste – che hanno tuttavia portato contributi significativi alla ricerca matematica''" (English translation:"''Added to these there are two works – never published in books or journals – that nevertheless have brought significant contributions to the research''").]
Articles
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Books
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*. A short course in the theory of functions of several complex variables, held in February 1972 at the
Centro Linceo Interdisciplinare di Scienze Matematiche e Loro Applicazioni "''Beniamino Segre''".
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*. The first volume of his selected works, collecting his and his coworkers contributions in ''algebraic geometry''.
*. The first part (''tomo'') of the second volume of his selected works, collecting his and his coworkers contributions to the theory of functions of ''several complex variables''.
*. The second part (''tomo'') of the second volume of his selected works, collecting his and his coworkers contributions to the theory of functions of ''several complex variables''.
*. The third and last volume of his selected works, collecting his and his coworkers contributions to the theory
partial differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and retur ...
s in the form of the study of ''complexes of differential operators''.
See also
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Bochner–Martinelli formula
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Chain complexes
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Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...
Notes
References
Biographical and general references
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*. Includes a publication list.
*. A "''
commemoration''" by a colleague and friend, including a publication list.
*. The biographical and bibliographical entry (updated up to 1976) on Aldo Andreotti, published under the auspices of the Accademia dei Lincei in a book collecting many profiles of its living members up to 1976.
*. Recollections on him by a coauthor, colleague and friend.
*. "''Recollection of Aldo Andreotti''" is the commemoration of Andreotti held by Vesentini at the
Sala degli Stemmi of the
Scuola Normale Superiore
The Scuola Normale Superiore in Pisa (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students.
It was founded in 1810 wi ...
on 2 May 1980.
*. The "''Premise''" by Vesentini to the second volume of Andreotti's Selecta.
Scientific references
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External links
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Aldo Andreotti
{{DEFAULTSORT:Andreotti, Aldo
1924 births
1980 deaths
20th-century Italian mathematicians
Complex analysts
University of Pisa alumni
Academic staff of the University of Pisa
Institute for Advanced Study visiting scholars
Members of the Lincean Academy
PDE theorists
Scientists from Florence
Scuola Normale Superiore di Pisa alumni
Members of the Göttingen Academy of Sciences and Humanities