{{short description|Italian mathematician (1924–1980)}} {{for-multi|the Italian sport shooter|Aldo Andreotti (sport shooter)|the racing driver|Aldo Andretti}} {{Infobox scientist | name = Aldo Andreotti | image = Aldo Andreotti.jpg | image_size = 280px | caption = Aldo Andreotti | birth_date = {{Birth date|1924|3|14|df=y}} | birth_place = Florence, Kingdom of Italy | death_date = {{Death date and age|1980|2|21|1924|3|14|df=y}} | death_place = Pisa, Italy | resting_place = San Francesco, Pisa | resting_place_coordinates = <!-- {{Coord|LAT|LONG|type:landmark|display=inline,title}} --> | fields = {{plainlist| *Algebraic Geometry *Several complex variables *Partial differential equations}} | workplaces = {{plainlist| *Institute for Advanced Study *Sapienza University of Rome *Scuola Normale Superiore}} | alma_mater = University of Pisa | thesis_title = | thesis_url = | thesis_year = | doctoral_advisor = Francesco Cecioni | academic_advisors = Francesco Severi | doctoral_students = | notable_students = | known_for = Andreotti–Vesentini theorem | author_abbrev_bot = | author_abbrev_zoo = | influences = | influenced = | awards = | signature = <!--(filename only)--> | signature_alt = | website = <!-- {{URL|www.example.com}} --> | footnotes = }} '''Aldo Andreotti''' (15 March 1924 – 21 February 1980) was an Italian mathematician who worked on algebraic geometry, on the theory of functions of several complex variables and on partial differential operators. Notably he proved the Andreotti–Frankel theorem, the Andreotti–Grauert theorem, the Andreotti–Vesentini theorem 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 in 1951 and again from 1957 through 1959.<ref>According to The Institute for Advanced Study|2012}}|Andreotti's Community of Scholars web site Profile and to {{harv|Mitchell|1980|p=50}}.</ref>
==Selected publications== Aldo Andreotti published 100 scientific works, including papers, books and lecture notes: many of them, except all his books but {{harv|Andreotti|Nacinovich|1980}}, are collected in his "''Selecta''" {{harvs|last=Andreotti|author-link=|year=1982|year2=1992|year3=1994|year4=1999}}. In his "Selecta" are also included three unpublished sets of lecture notes,<ref>See {{harv|Andreotti|1992|loc=pp. 383–432, 433–461 and 463–488}} and the premise to the volume by {{harvtxt|Vesentini|1992|p=5}}.</ref> 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,<ref>See {{harv|Andreotti|1992|pp=383–432}} and the premise to the volume by {{harvtxt|Vesentini|1992|p=5}}.</ref> the second and third ones taken from two lectures held by Francesco Gherardelli at the "Seminario di Geometria"<ref>The "Geometry Seminar" was a seminar on advanced geometry topics held at the Scuola Normale Superiore.</ref> of the Scuola Normale Superiore during the years 1971–1972 and 1971–1972 respectively, on topics concerning his joint work with Andreotti:<ref>See {{harv|Andreotti|1992|loc=pp. 433–461 and 463–488}} and the premise to the volume by {{harvtxt|Vesentini|1992|p=5}}.</ref> despite their nature of unpublished works, {{harvtxt|Vesentini|1992|p=5}} states that they have brought significant contributions to research.<ref>Precisely, {{harvtxt|Vesentini|1992|p=5}} 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''").</ref>
===Articles=== *{{Citation |last1 = Andreotti |first1 = Aldo |last2 = Grauert |first2 = Hans |author2-link = Hans Grauert |title = Théorèmes de finitude pour la cohomologie des espaces complexes |trans-title = Finiteness theorems for the cohomology of complex spaces |journal = Bulletin de la Société Mathématique de France |volume = 90 |pages = 193–259 |year = 1962 |doi = 10.24033/bsmf.1581 |language = fr |mr = 0150342 |zbl = 0106.05501 |doi-access = free }}. *{{Citation |last1 = Andreotti |first1 = Aldo |last2 =Vesentini |first2 =Edoardo |author2-link =Edoardo Vesentini |title =Carleman estimates for the Laplace-Beltrami equation on complex manifolds |journal =Publications Mathématiques de l'IHÉS |volume =25 |year =1965 |pages =81–130 |url =http://www.numdam.org/item?id=PMIHES_1965__25__81_0 |issn=1618-1913 |mr =0175148 |zbl =0138.06604 |doi=10.1007/bf02684398 |s2cid = 189796164 }}. *{{Citation |last1 = Andreotti |first1 = Aldo |last2 = Norguet |first2 = François |author2-link =François Norguet |title = Problème de Levi pour les classes de cohomologie |trans-title=The Levi problem for cohomology classes |journal = Comptes rendus hebdomadaires des séances de l'Académie des Sciences |volume = 258 |issue =Première partie |pages = 778–781 |date = 20 January 1964 |language = fr |url =http://gallica.bnf.fr/ark:/12148/bpt6k40102/f824.image |mr = 0159960 |zbl = 0124.38803 }}. *{{Citation |last1 = Andreotti |first1 = Aldo |last2 =Vesentini |first2 =Edoardo |author2-link =Edoardo Vesentini |title =Erratum. Carleman estimates for the Laplace-Beltrami equation on complex manifolds |journal =Publications Mathématiques de l'IHÉS |volume =27 |year =1965b |pages =153–155 |url =http://www.numdam.org/item?id=PMIHES_1965__27__153_0 |issn=1618-1913 |mr =0182983 |zbl =0138.06604 |doi=10.1007/bf02684376 |s2cid = 51858734 }}. *{{Citation |last1 = Andreotti |first1 = Aldo |last2 = Norguet |first2 = François |author2-link =François Norguet |title =Problème de Levi et convexité holomorphe pour les classes de cohomologie |trans-title=The Levi problem and holomorphic convexity for cohomology classes |journal =Annali della Scuola Normale Superiore di Pisa, Classe di Scienze |series = Serie III |volume =20 |issue =2 |pages =197–241 |year =1966 |language =fr |url =http://www.numdam.org/item?id=ASNSP_1966_3_20_2_197_0 |mr =199439 |zbl = 0154.33504 }}. *{{Citation |last1 = Andreotti |first1 = Aldo |last2 = Hill |first2 = C. Denson |author2-link = Clyde Denson Hill |title =E. E. Levi convexity and the Hans Lewy problem. Part I: reduction to vanishing theorems |journal =Annali della Scuola Normale Superiore di Pisa, Classe di Scienze |series = Serie III |volume =26 |issue =2 |pages =325–363 |year =1972 |url =http://www.numdam.org/item?id=ASNSP_1972_3_26_2_325_0 |mr =460725 }}. *{{Citation |last1 = Andreotti |first1 = Aldo |last2 = Hill |first2 = C. Denson |author2-link = Clyde Denson Hill |title =E. E. Levi convexity and the Hans Lewy problem. Part II: vanishing theorems |journal =Annali della Scuola Normale Superiore di Pisa, Classe di Scienze |series = Serie III |volume =26 |issue =4 |pages =747–806 |year =1972b |url =http://www.numdam.org/item?id=ASNSP_1972_3_26_4_747_0 |mr =477150 |zbl =0283.32013 }}.
===Books=== *{{Citation |last1 = Andreotti |first1 = Aldo |last2 = Stoll |first2 = Wilhelm |author2-link = Wilhelm Stoll |title = Analytic and Algebraic Dependence of Meromorphic Functions |place = Berlin–Heidelberg–New York |publisher = Springer-Verlag |series = Lecture Notes in Mathematics |volume = 234 |year = 1971 |pages = iii+390 |doi = 10.1007/BFb0058595 |isbn = 978-3-540-05670-6 |mr = 0390298 |zbl = 0222.32013 }}. *{{Citation |first = Aldo |last = Andreotti |editor-last = Gherardelli |editor-first = Francesco |contribution = Nine lectures on complex analysis |title = Complex Analysis. C.I.M.E. I Ciclo. Bressanone, 3–12 Giugno 1973 |series = C.I.M.E. Summer Schools |volume = 62 |year = 1974 |pages = 1–175 |place = Rome |publisher = Edizioni Cremonese |doi = 10.1007/978-3-642-10964-5_1 |isbn = 978-3-642-10963-8 |mr = 0442262 |zbl = 0353.32021 }}. *{{Citation |last = Andreotti |first = Aldo |title = Complexes of partial differential operators |place = New Haven, Conn. – London |publisher = Yale University Press |series = Yale Mathematical Monographs |volume = 6 |year = 1975 |pages = vi+49 |mr = 0413192 |zbl = 0309.58020 }}. *{{Citation |last = Andreotti |first = Aldo |title = Introduzione all'analisi complessa (Lezioni tenute nel febbraio 1972) |trans-title = Introduction to complex analysis (Lectures held in February 1972) |language = it |place = Rome |publisher = Accademia Nazionale dei Lincei |year = 1976 |series = Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche e Loro Applicazioni |volume = 24 |pages = 34 |url = http://www.lincei.it/pubblicazioni/catalogo/volume.php?lg=e&rid=33190 |access-date = 2012-10-20 |archive-url = https://web.archive.org/web/20120307131902/http://www.lincei.it/pubblicazioni/catalogo/volume.php?lg=e&rid=33190 |archive-date = 2012-03-07 |url-status = dead }}. 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''". *{{Citation |last = Andreotti |first = Aldo |title = Étude de géométrie algébrique |trans-title=Study of algebraic geometry |place = Strasbourg |publisher = Université Louis Pasteur, Département de Mathématique, Institut de Recherche Mathématique Avancée |year = 1978 |pages = 340 |language = fr |zbl = 0616.32001 }}. *{{Citation |last1 = Andreotti |first1 = Aldo |last2 = Nacinovich |first2 = Mauro |author2-link = Mauro Nacinovich |title = Analytic Convexity and the Principle of Phragmén–Lindelöf |place = Pisa |publisher=Edizioni della Normale |year = 1980 |series = Quaderni |pages = 184 |isbn =978-88-7642-243-0 |mr= 617737 |zbl = 0458.35004 }}, also published in {{harvnb|Andreotti|1999|pp=230–420}}. *{{Citation |last = Andreotti |first = Aldo |title = Geometrica algebrica |trans-title=Algebraic geometry |url = https://books.google.com/books?id=JcNUAAAAYAAJ |publisher = Scuola Normale Superiore |series = Selecta di opere |volume = I |place = Pisa |year = 1982 |pages = 424 |mr = 940467 }}. The first volume of his selected works, collecting his and his coworkers contributions in ''algebraic geometry''. *{{Citation |last = Andreotti |first = Aldo |title = Analisi complessa. Tomo I |trans-title=Several complex variables. Tome I |publisher = Scuola Normale Superiore |series = Selecta di opere |volume = II |place = Pisa |year = 1992 |pages = 1–488 }}. 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''. *{{Citation |last = Andreotti |first = Aldo |title = Analisi complessa. Tomo II |trans-title=Several complex variables. Tome II |publisher = Scuola Normale Superiore |series = Selecta di opere |volume = II |place = Pisa |year = 1994 |pages = 489–1144 }}. 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''. *{{Citation |last = Andreotti |first = Aldo |title = Complessi di operatori differenziali |trans-title=Complexes of differential operators |publisher = Scuola Normale Superiore |series = Selecta di opere |volume = III |place = Pisa |year = 1999 |pages = 633 }}. The third and last volume of his selected works, collecting his and his coworkers contributions to the theory partial differential operators in the form of the study of ''complexes of differential operators''.
==See also== *Bochner–Martinelli formula *Chain complexes *Cohomology
==Notes== {{reflist|30em}}
==References== {{refbegin}}
===Biographical and general references=== *{{Citation |last = Hill |first = C. Denson |author-link = Clyde Denson Hill |title = Aldo Andreotti |journal = Bollettino dell'Unione Matematica Italiana |series = Serie 9 |volume = 4 |issue = 2 |pages = 295–299 |url = http://www.bdim.eu/item?id=BUMI_2011_9_4_2_295_0 |year = 2011 |mr = 2840610 |zbl = 1228.01040 }}. *{{Citation |editor-last = Mitchell |editor-first = Janet A. |title = A Community of Scholars. Faculty and Members 1930-1980 |place = Princeton, New Jersey |publisher = The Institute for Advanced Study |year = 1980 |pages = xxii+565 |url = http://library.ias.edu/files/pdfs/hs/cos.pdf |access-date = 2012-10-20 |archive-date = 2017-11-07 |archive-url = https://web.archive.org/web/20171107021042/https://library.ias.edu/files/pdfs/hs/cos.pdf |url-status = dead }}. *{{Citation |last = The Institute for Advanced Study |author-link = Institute for Advanced Study |contribution = Andreotti, Aldo |contribution-url = https://www.ias.edu/scholars/aldo-andreotti |title = A Community of Scholars |year = 2012 |url = http://www.ias.edu/people/cos/ |access-date = 21 May 2016 }}. *{{Citation |last = The Editorial Board |title = List of publications by Aldo Andreotti |url = http://www.numdam.org/item?id=CM_1981__44_1-3_7_0 |year = 1981 |journal = Compositio Mathematica |issn = 0010-437X |volume = 44 |issue = 1 |pages = 7–15 |mr = 1557070 |zbl = 0476.01005 }} *{{Citation |last = Gherardelli |first = Francesco |title = Aldo Andreotti |year = 1981 |journal = Bollettino dell'Unione Matematica Italiana, Sezione A |series = Serie V |language = it |volume = 18 |issue = 2 |pages = 337–345 |mr = 618355 |zbl = 0457.01006 }}. Includes a publication list. *{{Citation |last = Huckleberry |first = Alan |author-link = Alan Huckleberry |title = Remembering Aldo Andreotti |journal = Bollettino dell'Unione Matematica Italiana |series = Serie 9 |volume = 4 |issue = 2 |pages = 307–309 |url = http://www.bdim.eu/item?id=BUMI_2011_9_4_2_295_0 |year = 2011 |mr = 2840622 |zbl = 1228.01041 }}. *{{citation |last = Marchionna |first = Ermanno |author-link = Ermanno Marchionna |title = Commemorazione di Aldo Andreotti |trans-title=Commemoration of Aldo Andreotti |language = it |journal = Atti della Accademia delle Scienze di Torino, Classe di Scienze Fisiche, Matematiche e Naturali |volume = 115 |year = 1981 |pages = 393–410 |mr = 0926790 |zbl = 0569.01015 }}. A "''commemoration''" by a colleague and friend, including a publication list. *{{Citation |editor-last =Ridolfi |editor-first =Roberto |contribution =Aldo Andreotti |title=Biografie e bibliografie degli Accademici Lincei |trans-title =Biographies and bibliographies of the Lincean Academicians |place =Rome |publisher =Accademia Nazionale dei Lincei |year =1976 |pages =59–61 |language =it }}. 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. *{{citation |first = Edoardo |last = Vesentini |author-link = Edoardo Vesentini |title = Aldo Andreotti |language = it |journal = Atti della Accademia Nazionale dei Lincei, Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali |volume = LXXI |series = Serie VIII |issue = 6 |date = December 1981 |url = http://www.bdim.eu/item?id=RLIN_1981_8_71_6_251_0 |pages = 253–258 |mr = 0703219 |zbl = 0504.01012 }}. Recollections on him by a coauthor, colleague and friend. *{{Citation |first = Edoardo |last = Vesentini |author-link = Edoardo Vesentini |editor-last = Andreotti |editor-first = Aldo |contribution = Ricordo di Aldo Andreotti |title = Geometrica algebrica |url = https://books.google.com/books?id=JcNUAAAAYAAJ |publisher = Scuola Normale Superiore |language = it |series = Selecta di opere |volume = I |place = Pisa |year = 1982 |pages = 7–16 }}. "''Recollection of Aldo Andreotti''" is the commemoration of Andreotti held by Vesentini at the Sala degli Stemmi of the Scuola Normale Superiore on 2 May 1980. *{{Citation |first = Edoardo |last = Vesentini |author-link = Edoardo Vesentini |editor-last = Andreotti |editor-first = Aldo |contribution = Premessa |title = Analisi complessa. Tomo I |url = https://books.google.com/books?id=JcNUAAAAYAAJ |publisher = Scuola Normale Superiore |language = it |series = Selecta di opere |volume = II |place = Pisa |year = 1992 |page = 5 }}. The "''Premise''" by Vesentini to the second volume of Andreotti's Selecta.
===Scientific references===
*{{Citation |last = Nacinovich |first = Mauro |author-link = Mauro Nacinovich |title = The Contribution of A. Andreotti to the Theory of Complexes of p.d.o.'s |journal = Bollettino dell'Unione Matematica Italiana |series = Serie 9 |volume = 4 |issue = 2 |pages = 301–306 |url = http://www.bdim.eu/item?id=BUMI_2011_9_4_2_301_0 |year = 2011 |mr = 2840621 |zbl = 1228.01044 }}. *{{Citation |last = Salmon |first = Paolo |author-link = Paolo Salmon |title = The Contribution of Aldo Andreotti to the Study of Algebra in Italy Around 1950 |journal = Bollettino dell'Unione Matematica Italiana |series = Serie 9 |volume = 4 |issue = 2 |pages = 285–294 |url = http://www.bdim.eu/item?id=BUMI_2011_9_4_2_301_0 |year = 2011 |mr = 2840609 |zbl = 1291.01026 }}. *{{Citation |last =Tarkhanov |first =Nikolai N. |author-link =Nikolai Tarkhanov |editor1-first=М. А. |editor1-last=Шубин |editor1-link=Mikhail Shubin (mathematician) |title =Метод параметрикса в теории дифференциальных комплексов |trans-title=The parametrix method in the theory of differential complexes |place =Novosibirsk |publisher =Наука |year =1990 |pages =248 |language =ru |isbn =5-02-028732-6 |mr =1082557 |zbl =0758.58002}} *{{Citation |last =Tarkhanov |first =Nikolai N. |author-link =Nikolai Tarkhanov |translator-first=P. M. |translator-last=Gauthier |title =Complexes of Differential Operators |place =Dordrecht–Boston–London |publisher =Kluwer Academic Publishers |series =Mathematics and Its Applications |volume =340 |orig-year =1990 |year =1995 |edition =translated and revised |pages =xviii+396 |doi =10.1007/978-94-011-0327-5 |isbn =0-7923-3706-9 |mr =1368856 |zbl =0852.58076 }}. {{refend}}
==External links== * {{MacTutor|id=Andreotti|title=Aldo Andreotti|date=July 2012}} * {{MathGenealogy|id=123741|title=Aldo Andreotti}} * [https://web.archive.org/web/20120229064140/http://www.dm.unito.it/sism/m_italiani/biografie/nastasi/andreotti.html Aldo Andreotti]
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{{DEFAULTSORT:Andreotti, Aldo}} Category:1924 births Category:1980 deaths Category:20th-century Italian mathematicians Category:Complex analysts Category:University of Pisa alumni Category:Academic staff of the University of Pisa Category:Institute for Advanced Study visiting scholars Category:Members of the Lincean Academy Category:Partial differential equation theorists Category:Scientists from Florence Category:Scuola Normale Superiore alumni Category:Members of the Göttingen Academy of Sciences and Humanities