Michael Atiyah

Michael Atiyah
Orientador(es)	William Vallance Douglas Hodge
Orientado(s)	Simon Donaldson, Kenneth David Elworthy, Lisa Jeffrey, Nigel Hitchin, Frances Kirwan, Peter Kronheimer, Ruth Lawrence, George Lusztig, Ian Robertson Porteous, John Roe, Graeme Segal, David Tall
Tese	1955: Some Applications of Topological Methods in Algebraic Geometry
[edite no Wikidata]

Michael Francis Atiyah, OM, FRS (Hampstead, Londres, 22 de abril de 1929 — 11 de janeiro de 2019), foi um matemático britânico de origem libanesa, considerado um dos expoentes da geometria do século XX.

Atiyah foi Professor Saviliano de Geometria em Oxford, mantendo esta carreira de 1963 até 1969, quando foi nomeado professor de matemática no Instituto de Estudos Avançados de Princeton.

Seu trabalho pioneiro em conjunto com Isadore Singer levou à prova do teorema do índice de Atiyah-Singer na década de 1960, resultado que serviu de base para o desenvolvimento de vários ramos da matemática desde então. Foi presidente da Sociedade Real de Edimburgo, de 2005 a 2008.

Também fundou, antes e conjuntamente com Friedrich Hirzebruch, o estudo de outra grande ferramenta da topologia algébrica: a K-teoria topológica. Foi inspirada pelo trabalho de Alexander Grothendieck ao generalizar o teorema de Riemann-Roch, e gerou a K-teoria algébrica e muitas aplicações em física matemática.

Bibliografia

Livros

Esta subseção lista todos os livros escritos por Atiyah; omite alguns livros que ele editou.

• Atiyah, Michael F.; Macdonald, Ian G. (1969), Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., MR 0242802 . A classic textbook covering standard commutative algebra.
• Atiyah, Michael F. (1970), Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Cologne: Westdeutscher Verlag, MR 0263102 . Reprinted as Predefinição:Harv.
• Atiyah, Michael F. (1974), Elliptic operators and compact groups, Lecture Notes in Mathematics, Vol. 401, Berlin, New York: Springer-Verlag, MR 0482866 . Reprinted as Predefinição:Harv.
• Atiyah, Michael F. (1979), Geometry of Yang–Mills fields, Scuola Normale Superiore Pisa, Pisa, MR 554924 . Reprinted as Predefinição:Harv.
• Atiyah, Michael F.; Hitchin, Nigel (1988), The geometry and dynamics of magnetic monopoles, ISBN 978-0-691-08480-0, M. B. Porter Lectures, Princeton University Press, MR 934202, doi:10.1515/9781400859306 . Reprinted as Predefinição:Harv.
• Atiyah, Michael F. (1988a), Collected works. Vol. 1 Early papers: general papers, ISBN 978-0-19-853275-0, Oxford Science Publications, The Clarendon Press Oxford University Press, MR 951892 .
• Atiyah, Michael F. (1988b), Collected works. Vol. 2 K-theory, ISBN 978-0-19-853276-7, Oxford Science Publications, The Clarendon Press Oxford University Press, MR 951892 .
• Atiyah, Michael F. (1988c), Collected works. Vol. 3 Index theory: 1, ISBN 978-0-19-853277-4, Oxford Science Publications, The Clarendon Press Oxford University Press, MR 951892 .
• Atiyah, Michael F. (1988d), Collected works. Vol. 4 Index theory: 2, ISBN 978-0-19-853278-1, Oxford Science Publications, The Clarendon Press Oxford University Press, MR 951892 .
• Atiyah, Michael F. (1988e), Collected works. Vol. 5 Gauge theories, ISBN 978-0-19-853279-8, Oxford Science Publications, The Clarendon Press Oxford University Press, MR 951892 .
• Atiyah, Michael F. (1989), K-theory, ISBN 978-0-201-09394-0, Advanced Book Classics 2nd ed. , Addison-Wesley, MR 1043170 . First edition (1967) reprinted as Predefinição:Harv.
• Atiyah, Michael F. (1990), The geometry and physics of knots, ISBN 978-0-521-39521-2, Lezioni Lincee. [Lincei Lectures], Cambridge University Press, MR 1078014, doi:10.1017/CBO9780511623868 . Reprinted as Predefinição:Harv.
• Atiyah, Michael F. (2004), Collected works. Vol. 6, ISBN 978-0-19-853099-2, Oxford Science Publications, The Clarendon Press Oxford University Press, MR 2160826 .
• Atiyah, Michael F. (2007), Siamo tutti matematici (Italian: We are all mathematicians), ISBN 978-88-8323-157-5, Roma: Di Renzo Editore, p. 96 
• Atiyah, Michael (2014), Collected works. Vol. 7. 2002-2013, ISBN 978-0-19-968926-2, Oxford Science Publications, The Clarendon Press Oxford University Press, MR 3223085 .
• Atiyah, Michael F.; Iagolnitzer, Daniel; Chong, Chitat (2015), Fields Medallists' Lectures (3rd Edition), ISBN 978-981-4696-18-0, World Scientific, doi:10.1142/9652 .

Artigos selecionados (em inglês)

• Atiyah, Michael F. (1961), «Characters and cohomology of finite groups», Inst. Hautes Études Sci. Publ. Math., 9: 23–64, doi:10.1007/BF02698718 . Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Hirzebruch, Friedrich (1961), «Vector bundles and homogeneous spaces», ISBN 9780821814031, Proc. Sympos. Pure Math. AMS, Proceedings of Symposia in Pure Mathematics, 3: 7–38, doi:10.1090/pspum/003/0139181 . Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Segal, Graeme B. (1969), «Equivariant K-Theory and Completion», Journal of Differential Geometry, 3 (1–2): 1–18, doi:10.4310/jdg/1214428815 . Reprinted in Predefinição:Harv.
• Atiyah, Michael F. (1976), «Elliptic operators, discrete groups and von Neumann algebras», Colloque "Analyse et Topologie" en l'Honneur de Henri Cartan (Orsay, 1974), Asterisque, 32–33, Soc. Math. France, Paris, pp. 43–72, MR 0420729 . Reprinted in Predefinição:Harv. Formulation of the Atiyah "Conjecture" on the rationality of the L²-Betti numbers.
• Atiyah, Michael F.; Singer, Isadore M. (1963), «The Index of Elliptic Operators on Compact Manifolds», Bull. Amer. Math. Soc., 69 (3): 322–433, doi:10.1090/S0002-9904-1963-10957-X . An announcement of the index theorem. Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Singer, Isadore M. (1968a), «The Index of Elliptic Operators I», Annals of Mathematics, 87 (3): 484–530, JSTOR 1970715, doi:10.2307/1970715 . This gives a proof using K theory instead of cohomology. Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Segal, Graeme B. (1968), «The Index of Elliptic Operators: II», Annals of Mathematics, Second Series, 87 (3): 531–545, JSTOR 1970716, doi:10.2307/1970716 . This reformulates the result as a sort of Lefschetz fixed point theorem, using equivariant K theory. Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Singer, Isadore M. (1968b), «The Index of Elliptic Operators III», Annals of Mathematics, Second Series, 87 (3): 546–604, JSTOR 1970717, doi:10.2307/1970717 . This paper shows how to convert from the K-theory version to a version using cohomology. Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Singer, Isadore M. (1971), «The Index of Elliptic Operators IV», Annals of Mathematics, Second Series, 93 (1): 119–138, JSTOR 1970756, doi:10.2307/1970756  This paper studies families of elliptic operators, where the index is now an element of the K-theory of the space parametrizing the family. Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Singer, Isadore M. (1971), «The Index of Elliptic Operators V», Annals of Mathematics, Second Series, 93 (1): 139–149, JSTOR 1970757, doi:10.2307/1970757 . This studies families of real (rather than complex) elliptic operators, when one can sometimes squeeze out a little extra information. Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Bott, Raoul (1966), «A Lefschetz Fixed Point Formula for Elliptic Differential Operators», Bull. Am. Math. Soc., 72 (2): 245–50, doi:10.1090/S0002-9904-1966-11483-0 . This states a theorem calculating the Lefschetz number of an endomorphism of an elliptic complex. Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Bott, Raoul (1967), «A Lefschetz Fixed Point Formula for Elliptic Complexes: I», Annals of Mathematics, Second Series, 86 (2): 374–407, JSTOR 1970694, doi:10.2307/1970694  (reprinted in Predefinição:Harv)and Atiyah, Michael F.; Bott, Raoul (1968), «A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications», Annals of Mathematics, Second Series, 88 (3): 451–491, JSTOR 1970721, doi:10.2307/1970721 . Reprinted in Predefinição:Harv. These give the proofs and some applications of the results announced in the previous paper.
• Atiyah, Michael F.; Bott, Raoul; Patodi, Vijay K. (1973), «On the heat equation and the index theorem» (PDF), Invent. Math., 19 (4): 279–330, Bibcode:1973InMat..19..279A, MR 0650828, doi:10.1007/BF01425417 ; Atiyah, Michael F.; Bott, R.; Patodi, V. K. (1975), «Errata», Invent. Math., 28 (3): 277–280, Bibcode:1975InMat..28..277A, MR 0650829, doi:10.1007/BF01425562  Reprinted in Predefinição:Harv.
• Atiyah, Michael F.; Schmid, Wilfried (1977), «A geometric construction of the discrete series for semisimple Lie groups», Invent. Math., 42: 1–62, Bibcode:1977InMat..42....1A, MR 0463358, doi:10.1007/BF01389783 ; Atiyah, Michael F.; Schmid, Wilfried (1979), «Erratum», Invent. Math., 54 (2): 189–192, Bibcode:1979InMat..54..189A, MR 0550183, doi:10.1007/BF01408936 . Reprinted in Predefinição:Harv.
• Atiyah, Michael (2010), Edinburgh Lectures on Geometry, Analysis and Physics, Bibcode:2010arXiv1009.4827A, arXiv:1009.4827v1 

Prêmios

• Medalha Fields (1966)
• Prêmio Internacional Rei Faisal (1987)
• Prêmio Abel (2004)

Referências

Ligações externas

• Predefinição:MathGenealogy
• «Gazeta Matemática - A Matemática no Século XX» (PDF) (em português) 
• «Unibocconi - A Michael F. Atiyah e Isadore M. Singer il Premio ABEL 2004» (em italiano) 

1. RedirecionamentoPredefinição:fim

Precedido por Lars Hörmander e John Milnor	Medalha Fields 1966 com Paul Cohen, Alexander Grothendieck e Stephen Smale	Sucedido por Alan Baker, Heisuke Hironaka, Sergei Novikov e John Griggs Thompson
Precedido por Joseph Hutchinson, John Zachary Young e Cecil Edgar Tilley	Medalha Real 1968 com Gilbert Roberts e Walter Thomas James Morgan	Sucedido por Charles William Oatley, Frederick Sanger e George Deacon
Precedido por Claude Ambrose Rogers	Medalha De Morgan 1980	Sucedido por Klaus Friedrich Roth
Precedido por Robert Hill	Medalha Copley 1988	Sucedido por César Milstein
Precedido por Jean-Pierre Serre	Prêmio Abel 2004 com Isadore Singer	Sucedido por Peter Lax

Presidentes da Royal Society
Século XVII	1660–1662: Robert Moray 1662–1677: William Brouncker 1677–1680: Joseph Williamson 1680–1682: Christopher Wren 1682–1683: John Hoskins 1683–1684: Cyril Wyche 1684–1686: Samuel Pepys 1686–1689: John Vaughan 1689–1690: Thomas Herbert 1690–1695: Robert Southwell 1695–1698: Charles Montagu
Século XVIII	1698–1703: John Somers 1703–1727: Isaac Newton 1727–1741: Hans Sloane 1741–1752: Martin Folkes 1752–1764: George Parker 1764–1768: James Douglas 1768: James Burrow 1768–1772: James West 1772: James Burrow 1772–1778: John Pringle
Século XIX	1778–1820: Joseph Banks 1820: William Hyde Wollaston 1820–1827: Humphry Davy 1827–1830: Davies Gilbert 1830–1838: Augustus Frederick 1838–1848: Joshua Alwyne Compton 1848–1854: William Parsons 1854–1858: John Wrottesley 1858–1861: Benjamin Collins Brodie 1861–1871: Edward Sabine 1871–1873: George Biddell Airy 1873–1878: Joseph Dalton Hooker 1878–1883: William Spottiswoode 1883–1885: Thomas Henry Huxley 1885–1890: George Gabriel Stokes 1890–1895: William Thomson 1895–1900: Joseph Lister
Século XX	1900–1905: William Huggins 1905–1908: John William Strutt 1908–1913: Archibald Geikie 1913–1915: William Crookes 1915–1920: Joseph John Thomson 1920–1925: Charles Scott Sherrington 1925–1930: Ernest Rutherford 1930–1935: Frederick Gowland Hopkins 1935–1940: William Henry Bragg 1940–1945: Henry Hallett Dale 1945–1950: Robert Robinson 1950–1955: Edgar Douglas Adrian 1955–1960: Cyril Norman Hinshelwood 1960–1965: Howard Walter Florey 1965–1970: Patrick Maynard Stuart Blackett 1970–1975: Alan Hodgkin 1975–1980: Alexander Todd 1980–1985: Andrew Huxley 1985–1990: George Porter 1990–1995: Michael Atiyah 1995–2000: Aaron Klug
Século XXI	2000–2005: Robert May 2005–2010: Martin Rees 2010–2015: Paul Nurse 2015–2020: Venkatraman Ramakrishnan 2020–: Adrian Smith

Predefinição:Presidentes da Sociedade Real de Edimburgo