Michael Atiyah

Sir Michael Francis Atiyah (n. 22 aprilie 1929, Greater London, Anglia, Regatul Unit – d. 11 ianuarie 2019, Edinburgh, Scoția, Regatul Unit) a fost un matematician britanic cu rădăcini libaneze, unul dintre cei mai importanți ai secolului XX.^[32]

Michael Atiyah
Date personale
Nume la naștere	Michael Francis Atiyah
Născut	22 aprilie 1929[1][2][3] Greater London, Anglia, Regatul Unit
Decedat	11 ianuarie 2019 (89 de ani)[2][3][4][5] Edinburgh, Scoția, Regatul Unit
Înmormântat	Binning Memorial Wood[*][[Binning Memorial Wood (cemetery in East Lothian, Scotland)|​]]
Părinți	Edward Atiyah[*][[Edward Atiyah (British writer and political activist)|​]][6]
Frați și surori	Patrick Atiyah[*][[Patrick Atiyah (jurist britanic)|​]][6]
Căsătorit cu	Lily (Brown) Atiyah[*][[Lily (Brown) Atiyah (Ph.D. University of Cambridge 1955)|​]][6]
Cetățenie	Regatul Unit[7]
Ocupație	matematician topolog[*]​ cadru didactic universitar[*]​
Locul desfășurării activității	Oxford[8] Cambridge[8]
Limbi vorbite	limba engleză[9][10][11]
Activitate
Domeniu	topologie matematică[12] geometrie[12]
Număr Erdős	4
Instituție	Universitatea Cambridge[6] Universitatea Oxford[6] Institute for Advanced Study[13] Universitatea din Edinburgh Armata Britanică[6] Institute for Advanced Study[6] Universitatea Oxford[6][14]
Alma Mater	Trinity College[6] The Manchester Grammar School[*][[The Manchester Grammar School (school in Manchester, UK)|​]][6] Universitatea Cambridge[15] Victoria College[*][[Victoria College (school in Alexandria, Egypt)|​]][6]
Organizații	Societatea Regală din Londra Academia Leopoldină Academia Franceză de Științe Det Norske Videnskaps-Akademi[*][[Det Norske Videnskaps-Akademi (academy of sciences)|​]] Accademia Nazionale dei Lincei American Mathematical Society[16][17] Academia Națională de Științe a Statelor Unite ale Americii[*]​[18] Academia Regală Suedeză de Științe Academia Națională de Științe a Ucrainei[*]​ Academia Americană de Arte și Științe[*]​ Academia Australiană de Științe[*]​ Academia Rusă de Științe Royal Society of Edinburgh[*][[Royal Society of Edinburgh (academy of sciences)|​]] Academia Națională Indiană de Științe[*]​ Academia Europaea[19] TWAS, the academy of sciences for the developing world[*][[TWAS, the academy of sciences for the developing world (merit-based science academy)|​]] American Philosophical Society[*]​
Conducător de doctorat	William Vallance Douglas Hodge[*]​[20][21]
Doctoranzi	Simon Donaldson[*]​[15] Nigel Hitchin[*]​[15] Graeme Segal[*][[Graeme Segal (mathematician)|​]][15] George Lusztig[22] Peter Benedict Kronheimer[*]​[22] Ian R. Porteous[*][[Ian R. Porteous (Scottish mathematician at the University of Liverpool and an educator on Merseyside (1930-2011))|​]][15] K. David Elworthy[*][[K. David Elworthy (matematician britanic)|​]][15] Lisa Jeffrey[*][[Lisa Jeffrey (matematiciană canadiană)|​]][15] Brian Joseph Sanderson[*]​[15] John Roe[*][[John Roe (matematician britanic)|​]][15] ...încă 15
Cunoscut pentru	teorema indicelui Atiyah–Singer[*]​ Atiyah algebroid[*][[Atiyah algebroid (Lie algebroid associated to a principal bundle)|​]] Atiyah–Hirzebruch spectral sequence[*][[Atiyah–Hirzebruch spectral sequence (computational tool from homological algebra)|​]] Atiyah–Segal completion theorem[*][[Atiyah–Segal completion theorem (Mathematical result about equivariant K-theory in homotopy theory)|​]] Atiyah–Hitchin–Singer theorem[*][[Atiyah–Hitchin–Singer theorem (the theorem that the space of SU(2) anti self dual Yang–Mills fields on a 4-sphere with index k > 0 has dimension 8k – 3)|​]] Atiyah–Bott fixed-point theorem[*][[Atiyah–Bott fixed-point theorem (theorem)|​]] Atiyah–Bott formula[*][[Atiyah–Bott formula |​]] Atiyah–Hitchin space[*][[Atiyah–Hitchin space (4-dimensional, asymptotically locally flat (ALF) hyperkähler manifold, which is the moduli space of two monopoles in the SU(2) Bogomolny equation)|​]] Atiyah-Jänich theorem[*][[Atiyah-Jänich theorem (mathematical theorem in functional analysis)|​]] Atiyah conjecture on configurations[*][[Atiyah conjecture on configurations (Mathematical conjecture)|​]] Atiyah–Jones conjecture[*][[Atiyah–Jones conjecture (theorem about the homology of the moduli space of instantons over a sphere, conjectured by M. F. Atiyah and J. D. S. Jones (1978), proved by C. P. Boyer, J. C. Hurtubise, and B. M. Mann et al. (1998, 1999))|​]] Atiyah conjecture[*][[Atiyah conjecture |​]]
Premii	Medalia Fields (1966) Medalia Copley (1988)[23] Premiul Abel (2004)[24] Royal Medal (1968)[6] King Faisal International Prize in Science[*][[King Faisal International Prize in Science |​]] (1987) De Morgan Medal[*][[De Morgan Medal (most prestigious award of the London Mathematical Society)|​]] (1980)[6] Josiah Willard Gibbs Lectureship[*][[Josiah Willard Gibbs Lectureship (American mathematics award (1923-))|​]] (1991)[6] grande médaille de l'Académie des sciences[*][[grande médaille de l'Académie des sciences |​]] (2010) Ordinul de Merit[*]​ (1992)[6] Royal Society Bakerian Medal[*][[Royal Society Bakerian Medal (English award in physical sciences)|​]] (1975) doctor honoris causa por la Universidad Politécnica de Cataluña[*][[doctor honoris causa por la Universidad Politécnica de Cataluña (Spanish award)|​]] (2008)[25] Berwick Prize[*][[Berwick Prize (award)|​]] (1961)[6] Čestný doktorát Univerzity Karlovy[*][[Čestný doktorát Univerzity Karlovy |​]] Corresponding Member of the Australian Academy of Science[*][[Corresponding Member of the Australian Academy of Science |​]] (1992) Fellow al Societății Regale din Edinburgh[*]​ Fellow of the Academy of Medical Sciences[*][[Fellow of the Academy of Medical Sciences (recognition)|​]] doctor honoris causa por la Universidad de Salamanca[*][[doctor honoris causa por la Universidad de Salamanca |​]] (1992)[26] Fellow of the American Mathematical Society[*][[Fellow of the American Mathematical Society (fellowship of the American Mathematical Society)|​]] (2013)[16][17] Membru al Academiei Americane de Arte și Științe[*]​ honorary doctor of the Chinese University of Hong Kong[*][[honorary doctor of the Chinese University of Hong Kong |​]] doctorado honoris causa por la Universidad Nacional Autónoma de México[*][[doctorado honoris causa por la Universidad Nacional Autónoma de México (award)|​]] Membru al Societății Regale Knight Bachelor[*][[Knight Bachelor (title granted to a man who has been knighted by the British monarch but not as a member of one of the organised orders of chivalry)|​]] (1983)[6] honorary Fellow of the Learned Society of Wales[*][[honorary Fellow of the Learned Society of Wales (fellowship)|​]] (2016)[27] IET Kelvin Lecture[*][[IET Kelvin Lecture (IET lecture)|​]] (2006) Gunning Victoria Jubilee Prize[*][[Gunning Victoria Jubilee Prize (Prize awarded by the Royal Society of Edinburgh)|​]] (1990)[6] President's Medal[*][[President's Medal (award from Institute of Physics)|​]] (2008)[28] Orden de Andrés Bello[*][[Orden de Andrés Bello |​]] (1997)[6] premiul Feltrinelli[*]​ (1981)[6] Medalia Benjamin Franklin[*]​ (1993)[6] Forder Lectureship[*][[Forder Lectureship (award conferred by the London and New Zealand Mathematical Societies (1987–))|​]] (1989)[29] Fellow of the Australian Academy of Science[*][[Fellow of the Australian Academy of Science (fellowship of the Australian Academy of Science)|​]] (1992)[30] doctor honoris causa (3 iunie 1995)[31]
Modifică date / text

Este cunoscut în special pentru lucrările sale de topologie algebrică și analiză matematică.

A colaborat cu mai mulți matematicieni, printre care Raoul Bott, Isadore Singer și Friedrich Hirzebruch. Cu acesta din urmă a pus bazele Teoriei K din domeniul spațiilor topologice. Dar cea mai valoroasă contribuție a sa o constituie Teorema indicelui Atiyah-Singer, care indică numărul de soluții independente ale anumitor tipuri de ecuații diferențiale.

Lucrări scrise

Cărți

Această subsecțiune enumeră toate cărțile scrise de Atiyah; omite câteva cărți pe care le-a editat.

• 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 (Atiyah 1988b, item 50).
• Atiyah, Michael F. (1974), Elliptic operators and compact groups, Lecture Notes in Mathematics, Vol. 401, Berlin, New York: Springer-Verlag, MR 0482866. Reprinted as (Atiyah 1988c, item 78).
• Atiyah, Michael F. (1979), Geometry of Yang–Mills fields, Scuola Normale Superiore Pisa, Pisa, MR 0554924. Reprinted as (Atiyah 1988e, item 99).
• Atiyah, Michael F.; Hitchin, Nigel (1988), The geometry and dynamics of magnetic monopoles, M. B. Porter Lectures, Princeton University Press, doi:10.1515/9781400859306, ISBN 978-0-691-08480-0, MR 0934202. Reprinted as (Atiyah 2004, item 126).
• Atiyah, Michael F. (1988), Collected works. Vol. 1 Early papers: general papers, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853275-0, MR 0951892.
• Atiyah, Michael F. (1988), Collected works. Vol. 2 K-theory, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853276-7, MR 0951892.
• Atiyah, Michael F. (1988), Collected works. Vol. 3 Index theory: 1, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853277-4, MR 0951892.
• Atiyah, Michael F. (1988), Collected works. Vol. 4 Index theory:2, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853278-1, MR 0951892.
• Atiyah, Michael F. (1988), Collected works. Vol. 5 Gauge theories, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853279-8, MR 0951892.
• Atiyah, Michael F. (1989), K-theory, Advanced Book Classics (ed. 2nd), Addison-Wesley, ISBN 978-0-201-09394-0, MR 1043170. First edition (1967) reprinted as (Atiyah 1988b, item 45).
• Atiyah, Michael F. (1990), The geometry and physics of knots, Lezioni Lincee. [Lincei Lectures], Cambridge University Press, doi:10.1017/CBO9780511623868, ISBN 978-0-521-39521-2, MR 1078014. Reprinted as (Atiyah 2004, item 136).
• Atiyah, Michael F. (2004), Collected works. Vol. 6, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853099-2, MR 2160826.
• Atiyah, Michael F. (2007), Siamo tutti matematici (Italian: We are all mathematicians), Roma: Di Renzo Editore, p. 96, ISBN 88-8323-157-0, arhivat din original la 14 ianuarie 2019, accesat în 13 ianuarie 2019
• Atiyah, Michael F.; Iagolnitzer, Daniel; Chong, Chitat (2015), Fields Medallists' Lectures (3rd Edition), World Scientific, ISBN 978-981-4696-18-0.

Lucrări selectate

• 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 (Atiyah 1988b, paper 29).
• Atiyah, Michael F.; Hirzebruch, Friedrich (1961), „Vector bundles and homogeneous spaces”, Proc. Sympos. Pure Math. AMS, 3: 7–38. Reprinted in (Atiyah 1988b, paper 28).
• Atiyah, Michael F.; Segal, Graeme B. (1969), „Equivariant K-Theory and Completion”, Journal of Differential Geometry, 3: 1–18. Reprinted in (Atiyah 1988b, paper 49).
• 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 (Atiyah 1988d, paper 89). 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: 322–433, doi:10.1090/S0002-9904-1963-10957-X. An announcement of the index theorem. Reprinted in (Atiyah 1988c, paper 56).
• Atiyah, Michael F.; Singer, Isadore M. (1968), „The Index of Elliptic Operators I”, Annals of Mathematics, The Annals of Mathematics, Vol. 87, No. 3, 87 (3): 484–530, doi:10.2307/1970715, JSTOR 1970715. This gives a proof using K theory instead of cohomology. Reprinted in (Atiyah 1988c, paper 64).
• Atiyah, Michael F.; Segal, Graeme B. (1968), „The Index of Elliptic Operators: II”, Annals of Mathematics, Second Series, The Annals of Mathematics, Vol. 87, No. 3, 87 (3): 531–545, doi:10.2307/1970716, JSTOR 1970716. This reformulates the result as a sort of Lefschetz fixed point theorem, using equivariant K theory. Reprinted in (Atiyah 1988c, paper 65).
• Atiyah, Michael F.; Singer, Isadore M. (1968), „The Index of Elliptic Operators III”, Annals of Mathematics, Second Series, 87 (3): 546–604, doi:10.2307/1970717, JSTOR 1970717. This paper shows how to convert from the K-theory version to a version using cohomology. Reprinted in (Atiyah 1988c, paper 66).
• Atiyah, Michael F.; Singer, Isadore M. (1971), „The Index of Elliptic Operators IV”, Annals of Mathematics, Second Series, The Annals of Mathematics, Vol. 93, No. 1, 93 (1): 119–138, doi:10.2307/1970756, JSTOR 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 (Atiyah 1988c, paper 67).
• Atiyah, Michael F.; Singer, Isadore M. (1971), „The Index of Elliptic Operators V”, Annals of Mathematics, Second Series, The Annals of Mathematics, Vol. 93, No. 1, 93 (1): 139–149, doi:10.2307/1970757, JSTOR 1970757. This studies families of real (rather than complex) elliptic operators, when one can sometimes squeeze out a little extra information. Reprinted in (Atiyah 1988c, paper 68).
• 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 (Atiyah 1988c, paper 61).
• Atiyah, Michael F.; Bott, Raoul (1967), „A Lefschetz Fixed Point Formula for Elliptic Complexes: I”, Annals of Mathematics, Second Series, The Annals of Mathematics, Vol. 86, No. 2, 86 (2): 374–407, doi:10.2307/1970694, JSTOR 1970694 (reprinted in (Atiyah 1988c, paper 61))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, doi:10.2307/1970721, JSTOR 1970721. Reprinted in (Atiyah 1988c, paper 62). 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, doi:10.1007/BF01425417, MR 0650828; Atiyah, Michael F.; Bott, R.; Patodi, V. K. (1975), „Errata”, Invent. Math., 28 (3): 277–280, Bibcode:1975InMat..28..277A, doi:10.1007/BF01425562, MR 0650829 Reprinted in (Atiyah 1988d, paper 79, 79a).
• 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, doi:10.1007/BF01389783, MR 0463358; Atiyah, Michael F.; Schmid, Wilfried (1979), „Erratum”, Invent. Math., 54 (2): 189–192, Bibcode:1979InMat..54..189A, doi:10.1007/BF01408936, MR 0550183. Reprinted in (Atiyah 1988d, paper 90).
• Atiyah, Michael (2010), Edinburgh Lectures on Geometry, Analysis and Physics (PDF)

Premii și distincții

• 1966: Medalia Fields
• 1968: Royal Medal din partea Royal Society
• 1981: Premiul Antonio-Feltrinelli din partea Accademia Nazionale dei Lincei
• 1987: Premiul Internațional König-Faisal pentru Știință
• 1983: numit cavaler
• 1988: Medalia Copley
• 1992: devine membru al ordinului britanic Order of Merit
• 2004: Premiul Abel.