M. F. Atiyah and N. J. Hitchin :
“Low energy scattering of nonabelian monopoles Phys. Lett. A
107 : 1
(1985 ),
pp. 21–25 .
MR
778313 Zbl
1177.53069 article
Abstract
People
BibTeX
@article {key778313m,
AUTHOR = {Atiyah, M. F. and Hitchin, N. J.},
TITLE = {Low energy scattering of nonabelian
monopoles},
JOURNAL = {Phys. Lett. A},
FJOURNAL = {Physics Letters A},
VOLUME = {107},
NUMBER = {1},
YEAR = {1985},
PAGES = {21--25},
DOI = {10.1016/0375-9601(85)90238-5},
NOTE = {MR:778313. Zbl:1177.53069.},
ISSN = {0375-9601},
}
M. Atiyah, N. J. Hitchin, J. T. Stuart, and M. Tabor :
“Low-energy scattering of nonabelian magnetic monopoles [and discussion] Philos. Trans. Roy. Soc. London Ser. A
315 : 1533
(1985 ),
pp. 459–469 .
MR
836746 article
Abstract
People
BibTeX
The Bogomolny equations represent static configurations of magnetic monopoles, for some non-Abelian group such as \( \mathit{SU}(2) \) . Geodesic motion on this configuration space represents slowly moving interacting monopoles. Geometric information on this space can then be used to investigate the scattering of monopoles. The results show surprising features, including a 90 degrees scattering and the conversion of angular momentum into electric charge.
@article {key836746m,
AUTHOR = {Atiyah, Michael and Hitchin, N. J. and
Stuart, J. T. and Tabor, M.},
TITLE = {Low-energy scattering of nonabelian
magnetic monopoles [and discussion]},
JOURNAL = {Philos. Trans. Roy. Soc. London Ser.
A},
FJOURNAL = {Philosophical Transactions of the Royal
Society A: Mathematical, Physical \&
Engineering Sciences},
VOLUME = {315},
NUMBER = {1533},
YEAR = {1985},
PAGES = {459--469},
DOI = {10.1098/rsta.1985.0052},
NOTE = {MR:836746.},
ISSN = {0080-4614},
}
M. Atiyah :
“On the work of Simon Donaldson 3–6
in
Proceedings of the International Congress of Mathematicians
(Berkeley, CA, 3–11 August 1986 ),
vol. 2 .
Edited by A. Gleason .
American Mathematical Society (Providence, RI ),
1987 .
MR
934209 Zbl
0666.01010 incollection
People
BibTeX
@incollection {key934209m,
AUTHOR = {Atiyah, Michael},
TITLE = {On the work of {S}imon {D}onaldson},
BOOKTITLE = {Proceedings of the {I}nternational {C}ongress
of {M}athematicians},
EDITOR = {Andrew Gleason},
VOLUME = {2},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1987},
PAGES = {3--6},
URL = {http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0003.0006.ocr.pdf},
NOTE = {(Berkeley, CA, 3--11 August 1986). MR:934209.
Zbl:0666.01010.},
ISBN = {9780821801109},
}
M. Atiyah :
“The logarithm of the Dedekind \( \eta \) -function Math. Ann.
278 : 1–4
(1987 ),
pp. 335–380 .
MR
909232 Zbl
0648.58035 article
BibTeX
@article {key909232m,
AUTHOR = {Atiyah, Michael},
TITLE = {The logarithm of the {D}edekind \$\eta\$-function},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {278},
NUMBER = {1--4},
YEAR = {1987},
PAGES = {335--380},
DOI = {10.1007/BF01458075},
NOTE = {MR:909232. Zbl:0648.58035.},
ISSN = {0025-5831},
}
M. Atiyah :
“Topology and differential equations ,”
pp. 45–52
in
ICIAM ’87: Proceedings of the first International Conference on Industrial and Applied Mathematics
(Paris, 29 June–3 July 1987 ).
Edited by J. McKenna and R. Temam .
SIAM (Philadelphia, PA ),
1988 .
MR
976850 Zbl
0687.35001 incollection
Abstract
People
BibTeX
In many areas of differential equations topological methods can provide important qualitative information. This particularly applies to complicated problems where the number of variables is large. Examples will be given illustrating the scope and power of topological ideas.
For constant coefficient linear hyperbolic systems the fundamental solution is supported in the forward “light-cone”. For general systems this cone has many compartments and, in some of these (called lacunas) the fundamental solution may vanish. The determination of lacunas is a topological problem (solved originally by Petrovsky) involving the topology of multi-dimensional contour integrals in the complex domain.
For elliptic boundary value problems of Cauchy–Riemann or Dirac type the index, measuring the difference between the number of solutions of the problem and its adjoint, is a topological invariant which can be computed from the geometrical data. This has important applications to models in elementary particle physics.
For a periodic family of self-adjoint elliptic operators the spectral flow, counting the net number of eigenvalues which change sign over a period, is a topological invariant. This can be computed from the geometrical data and can be used to derive sharp bounds on gaps in the spectrum.
In non-linear PDE, “solitons” may have a topological origin, and soliton-interaction can be related to underlying topological features. This is illustrated by models in 2 and 3 spatial dimensions, following original ideas of Skyrme.
@incollection {key976850m,
AUTHOR = {Atiyah, Michael},
TITLE = {Topology and differential equations},
BOOKTITLE = {I{CIAM} '87: {P}roceedings of the first
{I}nternational {C}onference on {I}ndustrial
and {A}pplied {M}athematics},
EDITOR = {James McKenna and Roger Temam},
PUBLISHER = {SIAM},
ADDRESS = {Philadelphia, PA},
YEAR = {1988},
PAGES = {45--52},
NOTE = {(Paris, 29 June--3 July 1987). MR:976850.
Zbl:0687.35001.},
ISBN = {9780898712247},
}
M. Atiyah :
“New invariants of 3- and 4-dimensional manifolds ,”
pp. 285–299
in
The mathematical heritage of Hermann Weyl
(Durham, NC, 12–16 May 1987 ).
Edited by R. O. Wells, Jr.
Proceedings of Symposia in Pure Mathematics 48 .
American Mathematical Society (Providence, RI ),
1988 .
Russian translation published in Uspekhi Mat. Nauk 45 :4(274) (1990)
MR
974342 Zbl
0667.57018 incollection
Abstract
People
BibTeX
In this talk I am going to describe some of the most recent, and still incomplete, developments involving the application of ideas from the physics of gauge theories to the study of manifolds in 3 and 4 dimensions. The main results are due to S. K. Donaldson who initiated the whole programme a few years ago, but important contributions are being made by C. Taubes and A. Floer. Moreover mathematicians have learnt a great deal about the geometrical interpretation of physical ideas from E. Witten.
@incollection {key974342m,
AUTHOR = {Atiyah, Michael},
TITLE = {New invariants of 3- and 4-dimensional
manifolds},
BOOKTITLE = {The mathematical heritage of {H}ermann
{W}eyl},
EDITOR = {Wells, Jr., R. O.},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {48},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1988},
PAGES = {285--299},
NOTE = {(Durham, NC, 12--16 May 1987). Russian
translation published in \textit{Uspekhi
Mat. Nauk} \textbf{45}:4(274) (1990).
MR:974342. Zbl:0667.57018.},
ISSN = {0082-0717},
ISBN = {9780821814826},
}
M. Atiyah :
“Topological quantum field theories Inst. Hautes Études Sci. Publ. Math.
68 : 1
(January 1988 ),
pp. 175–186 .
MR
1001453 Zbl
0692.53053 article
BibTeX
@article {key1001453m,
AUTHOR = {Atiyah, Michael},
TITLE = {Topological quantum field theories},
JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
FJOURNAL = {Publications Math\'ematiques de l'Institut
des Hautes \'Etudes Scientifiques},
VOLUME = {68},
NUMBER = {1},
MONTH = {January},
YEAR = {1988},
PAGES = {175--186},
DOI = {10.1007/BF02698547},
URL = {http://www.numdam.org/item?id=PMIHES_1988__68__175_0},
NOTE = {MR:1001453. Zbl:0692.53053.},
ISSN = {0073-8301},
}
M. Atiyah and N. Hitchin :
The geometry and dynamics of magnetic monopoles .
M. B. Porter Lectures .
Princeton University Press ,
1988 .
Russian translation published as Geometriya i dinamika magnitnykh monopolei (1991)
MR
934202 Zbl
0671.53001 book
People
BibTeX
@book {key934202m,
AUTHOR = {Atiyah, Michael and Hitchin, Nigel},
TITLE = {The geometry and dynamics of magnetic
monopoles},
SERIES = {M.~B. Porter Lectures},
PUBLISHER = {Princeton University Press},
YEAR = {1988},
PAGES = {viii+134},
NOTE = {Russian translation published as \textit{Geometriya
i dinamika magnitnykh monopolei} (1991).
MR:934202. Zbl:0671.53001.},
ISBN = {9780691084800},
}
M. F. Atiyah :
“Geometry, topology and physics Quart. Journ. Royal Astrophysics Soc.
29 : 3
(September 1988 ),
pp. 287–299 .
Delivered as the 11th Arthur Milne Lecture at Oxford University.
Republished in Atiyah’s Collected works , vol. 6 .
article
Abstract
BibTeX
The relation between Geometry and Physics is a very ancient one going back to the earliest times, but in the modern period it is best exemplified by Einstein’s Theory of General Relativity. As is well known, Einstein interpreted gravitational force in terms of the curvature of space-time and Maxwell’s Theory of Electro-Magnetism was subsequently interpreted in a somewhat similar manner. At the presetnt time these geometrical ideas have been extended to incorporate the other fundamental forces of nature, the “weak” and “strong” forces that are encountered at the nuclear level. As a result we are witnessing now a remarkable interaction between mathematicians and physicists which has been extremely fruitful.
@article {key59810722,
AUTHOR = {Atiyah, M. F.},
TITLE = {Geometry, topology and physics},
JOURNAL = {Quart. Journ. Royal Astrophysics Soc.},
FJOURNAL = {The Quarterly journal of the Royal Astronomical
Society},
VOLUME = {29},
NUMBER = {3},
MONTH = {September},
YEAR = {1988},
PAGES = {287--299},
URL = {http://adsabs.harvard.edu/full/1988QJRAS.29.287A},
NOTE = {Delivered as the 11th Arthur Milne Lecture
at Oxford University. Republished in
Atiyah's \textit{Collected works}, vol.~6.},
ISSN = {0035-8738},
}
M. Atiyah and G. Segal :
“On equivariant Euler characteristics J. Geom. Phys.
6 : 4
(1989 ),
pp. 671–677 .
MR
1076708 Zbl
0708.19004 article
Abstract
People
BibTeX
@article {key1076708m,
AUTHOR = {Atiyah, Michael and Segal, Graeme},
TITLE = {On equivariant {E}uler characteristics},
JOURNAL = {J. Geom. Phys.},
FJOURNAL = {Journal of Geometry and Physics},
VOLUME = {6},
NUMBER = {4},
YEAR = {1989},
PAGES = {671--677},
DOI = {10.1016/0393-0440(89)90032-6},
NOTE = {MR:1076708. Zbl:0708.19004.},
ISSN = {0393-0440},
}
M. F. Atiyah and N. S. Manton :
“Skyrmions from instantons Phys. Lett. B
222 : 3–4
(1989 ),
pp. 438–442 .
MR
1001325 article
Abstract
People
BibTeX
@article {key1001325m,
AUTHOR = {Atiyah, M. F. and Manton, N. S.},
TITLE = {Skyrmions from instantons},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters B},
VOLUME = {222},
NUMBER = {3--4},
YEAR = {1989},
PAGES = {438--442},
DOI = {10.1016/0370-2693(89)90340-7},
NOTE = {MR:1001325.},
ISSN = {0370-2693},
}
M. F. Atiyah :
“The geometry and physics of knots ,”
pp. 1–17
in
Miniconference on geometry and physics
(Canberra, 20–23 February 1989 ).
Edited by M. N. Barber and M. K. Murray .
Proceedings of the Centre for Mathematical Analysis 22 .
Australian National University (Canberra ),
1989 .
See also 1990 book of the same title .
MR
1027859 Zbl
0696.57002 incollection
People
BibTeX
@incollection {key1027859m,
AUTHOR = {Atiyah, M. F.},
TITLE = {The geometry and physics of knots},
BOOKTITLE = {Miniconference on geometry and physics},
EDITOR = {Michael N. Barber and Michael K. Murray},
SERIES = {Proceedings of the Centre for Mathematical
Analysis},
NUMBER = {22},
PUBLISHER = {Australian National University},
ADDRESS = {Canberra},
YEAR = {1989},
PAGES = {1--17},
NOTE = {(Canberra, 20--23 February 1989). See
also 1990 book of the same title. MR:1027859.
Zbl:0696.57002.},
ISBN = {9780731504350},
}
M. Atiyah :
“New invariants of 3- and 4-dimensional manifolds ,”
Uspekhi Mat. Nauk
45 : 4(274)
(1990 ),
pp. 3–16, 192 .
Russian translation of article from The mathematical heritage of Hermann Weyl (1988)
MR
1075385 Zbl
0709.57018 article
BibTeX
@article {key1075385m,
AUTHOR = {Atiyah, M.},
TITLE = {New invariants of 3- and 4-dimensional
manifolds},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk},
VOLUME = {45},
NUMBER = {4(274)},
YEAR = {1990},
PAGES = {3--16, 192},
NOTE = {Russian translation of article from
\textit{The mathematical heritage of
Hermann Weyl} (1988). MR:1075385. Zbl:0709.57018.},
ISSN = {0042-1316},
}
M. Atiyah :
“On framings of 3-manifolds Topology
29 : 1
(1990 ),
pp. 1–7 .
MR
1046621 Zbl
0716.57011 article
Abstract
BibTeX
@article {key1046621m,
AUTHOR = {Atiyah, Michael},
TITLE = {On framings of 3-manifolds},
JOURNAL = {Topology},
FJOURNAL = {Topology},
VOLUME = {29},
NUMBER = {1},
YEAR = {1990},
PAGES = {1--7},
DOI = {10.1016/0040-9383(90)90021-B},
NOTE = {MR:1046621. Zbl:0716.57011.},
ISSN = {0040-9383},
}
M. Atiyah :
The geometry and physics of knots Lezioni Lincee .
Cambridge University Press ,
1990 .
These notes arise from lectures presented in Florence under the auspices of the Accademia dei Lincei.
Russian translation published as Geometriya i fizika uzlov (1995)Miniconference on geometry and physics (1989)
MR
1078014 Zbl
0729.57002 book
BibTeX
@book {key1078014m,
AUTHOR = {Atiyah, Michael},
TITLE = {The geometry and physics of knots},
SERIES = {Lezioni Lincee},
PUBLISHER = {Cambridge University Press},
YEAR = {1990},
PAGES = {78},
DOI = {10.1017/CBO9780511623868},
NOTE = {These notes arise from lectures presented
in {F}lorence under the auspices of
the {A}ccademia dei {L}incei. Russian
translation published as \textit{Geometriya
i fizika uzlov} (1995). See also \textit{Miniconference
on geometry and physics} (1989). MR:1078014.
Zbl:0729.57002.},
ISBN = {9780521395540},
}
M. F. Atiyah and L. Jeffrey :
“Topological Lagrangians and cohomology J. Geom. Phys.
7 : 1
(1990 ),
pp. 119–136 .
MR
1094734 Zbl
0721.58056 article
Abstract
People
BibTeX
Witten [1988] has interpreted the Donaldson invariants of four-manifolds by means of a topological Lagrangian. We show that this Lagrangian should be understood in terms of an infinite-dimensional analogue of the Gauss–Bonnet formula. Starting with a formula of Mathai and Quillen for the Thom class, we obtain a formula for the Euler class of a vector bundle, which formally yields the explicit form of Witten’s Lagrangian. We use the same method to treat Lagrangians proposed for the Casson invariant.
@article {key1094734m,
AUTHOR = {Atiyah, M. F. and Jeffrey, L.},
TITLE = {Topological {L}agrangians and cohomology},
JOURNAL = {J. Geom. Phys.},
FJOURNAL = {Journal of Geometry and Physics},
VOLUME = {7},
NUMBER = {1},
YEAR = {1990},
PAGES = {119--136},
DOI = {10.1016/0393-0440(90)90023-V},
NOTE = {MR:1094734. Zbl:0721.58056.},
ISSN = {0393-0440},
}
M. Atiyah :
“Hyper-Kähler manifolds 1–13
in
Complex geometry and analysis
(Pisa, 23–27 May 1988 ).
Edited by V. Villani .
Lecture Notes in Mathematics 1422 .
Springer (Berlin ),
1990 .
MR
1055838 incollection
Abstract
People
BibTeX
In recent years hyperkähler manifolds have turned up in a wide variety of contexts, and it now becoming clear that they form a very interesting class of manifolds with a rich theory. The purpose of this lecture is to justify these claims by giving an overall survey of the field.
@incollection {key1055838m,
AUTHOR = {Atiyah, Michael},
TITLE = {Hyper-{K}\"ahler manifolds},
BOOKTITLE = {Complex geometry and analysis},
EDITOR = {Vinicio Villani},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1422},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1990},
PAGES = {1--13},
DOI = {10.1007/BFb0089400},
NOTE = {(Pisa, 23--27 May 1988). MR:1055838.},
ISSN = {0075-8434},
ISBN = {9783540524342},
}
M. Atiyah :
“Magnetic monopoles and the Yang–Baxter equations 2761–2774
in
Topological methods in quantum field theory
(Trieste, 11–15 June 1990 ),
published as Internat. J. Modern Phys. A
6 : 16
(1991 ).
MR
1117746 Zbl
0757.53038 incollection
Abstract
BibTeX
A comparison is made between the new solutions of the Yang–Baxter equations, arising from curves of higher genus, and magnetic monopoles of higher charge. It is shown that essentially the same algebraic curves arise in both cases, and this leads to speculations about possibly more general solutions of the Yang–Baxter equations.
@article {key1117746m,
AUTHOR = {Atiyah, Michael},
TITLE = {Magnetic monopoles and the {Y}ang--{B}axter
equations},
JOURNAL = {Internat. J. Modern Phys. A},
FJOURNAL = {International Journal of Modern Physics
A},
VOLUME = {6},
NUMBER = {16},
YEAR = {1991},
PAGES = {2761--2774},
DOI = {10.1142/S0217751X91001349},
NOTE = {\textit{Topological methods in quantum
field theory} (Trieste, 11--15 June
1990). MR:1117746. Zbl:0757.53038.},
ISSN = {0217-751X},
ISBN = {9789810204969},
}
M. Atiyah and N. Khitchin :
Geometriya i dinamika magnitnykh monopolei
[The geometry and dynamics of magnetic monopoles ].
Mir (Moscow ),
1991 .
Russian translation of The geometry and dynamics of magnetic monopoles (1988)
MR
1137269 Zbl
0754.53003 book
People
BibTeX
@book {key1137269m,
AUTHOR = {Atiyah, M. and Khitchin, N.},
TITLE = {Geometriya i dinamika magnitnykh monopolei
[The geometry and dynamics of magnetic
monopoles]},
PUBLISHER = {Mir},
ADDRESS = {Moscow},
YEAR = {1991},
PAGES = {150},
NOTE = {Russian translation of \textit{The geometry
and dynamics of magnetic monopoles}
(1988). MR:1137269. Zbl:0754.53003.},
ISBN = {9785030017945},
}
M. Atiyah :
“On the work of Edward Witten ,”
pp. 31–35
in
Proceedings of the International Congress of Mathematicians
(Kyoto, 21–29 August 1990 ),
vol. 1 .
Edited by I. Satake .
Mathematical Society of Japan (Tokyo ),
1991 .
MR
1159202 Zbl
0742.01013 incollection
People
BibTeX
@incollection {key1159202m,
AUTHOR = {Atiyah, Michael},
TITLE = {On the work of {E}dward {W}itten},
BOOKTITLE = {Proceedings of the {I}nternational {C}ongress
of {M}athematicians},
EDITOR = {Satake, Ichir\=o},
VOLUME = {1},
PUBLISHER = {Mathematical Society of Japan},
ADDRESS = {Tokyo},
YEAR = {1991},
PAGES = {31--35},
NOTE = {(Kyoto, 21--29 August 1990). MR:1159202.
Zbl:0742.01013.},
ISBN = {9784431700470},
}
M. F. Atiyah :
“Mathematics: Queen and servant of the sciences Proc. Am. Phil. Soc.
137 : 4
(December 1993 ),
pp. 527–531 .
250th anniversary issue.
Republished in Asian J. Math. 3 :1 (1999)The founders of index theory (2009)
article
BibTeX
@article {key30378029,
AUTHOR = {Atiyah, Michael F.},
TITLE = {Mathematics: {Q}ueen and servant of
the sciences},
JOURNAL = {Proc. Am. Phil. Soc.},
FJOURNAL = {Proceedings of the American Philosophical
Society},
VOLUME = {137},
NUMBER = {4},
MONTH = {December},
YEAR = {1993},
PAGES = {527--531},
URL = {http://www.jstor.org/stable/987071},
NOTE = {250th anniversary issue. Republished
in \textit{Asian J. Math.} \textbf{3}:1
(1999) and \textit{The founders of index
theory} (2009).},
ISSN = {0003-049X},
}
M. F. Atiyah and N. S. Manton :
“Geometry and kinematics of two skyrmions Comm. Math. Phys.
153 : 2
(1993 ),
pp. 391–422 .
MR
1218307 Zbl
0778.53051 article
Abstract
People
BibTeX
In Skyrme’s soliton model of baryons, a single Skyrmion has six degrees of freedom, so it is expected that two-Skyrmion dynamics at modest energies can be modelled by motion on a 12-dimensional space of Skyrme fields. A candidate for this space is generated by the gradient flow of the potential energy function, descending from the unstable, baryon number two, hedgehog solutions of the Skyrme field equation. An apparently very similar space is obtained by restricting the gradient flow to the Skyrme fields derived from \( \mathit{SU}(2) \) Yang–Mills instantons of charge two. On both of these spaces, one may quotient out by the group of translations and isospin rotations. Hartshome’s geometrical description of charge two instantons leads us to a conjecture for the global structure of the 6-dimensional quotient space. The conjectured structure is that of complex projective 3-space, with complex conjugate points on one projective plane identified and the real points in this plane removed.
@article {key1218307m,
AUTHOR = {Atiyah, M. F. and Manton, N. S.},
TITLE = {Geometry and kinematics of two skyrmions},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {153},
NUMBER = {2},
YEAR = {1993},
PAGES = {391--422},
DOI = {10.1007/BF02096649},
URL = {http://projecteuclid.org/getRecord?id=euclid.cmp/1104252686},
NOTE = {MR:1218307. Zbl:0778.53051.},
ISSN = {0010-3616},
}
M. F. Atiyah :
“American Philosophical Society dinner address, 30 April 1993 ,”
Proc. Am. Phil. Soc.
137 : 4
(1993 ),
pp. 704–707 .
Republished in Atiyah’s Collected works , vol. 6 .
article
BibTeX
@article {key37820997,
AUTHOR = {Atiyah, M. F.},
TITLE = {American {P}hilosophical {S}ociety dinner
address, 30 {A}pril 1993},
JOURNAL = {Proc. Am. Phil. Soc.},
FJOURNAL = {Proceedings of the American Philosophical
Society},
VOLUME = {137},
NUMBER = {4},
YEAR = {1993},
PAGES = {704--707},
NOTE = {Republished in Atiyah's \textit{Collected
works}, vol.~6.},
ISSN = {0003-049X},
}
M. F. Atiyah :
“Anniversary address by the President ,”
Royal Society News
supplement
(December 1994 ),
pp. i–iv, 535–540 .
Republished in Atiyah’s Collected works , vol. 6 . See also version in Notes and Records Roy. Soc. London 49 :1 (1995)
article
BibTeX
@article {key34065526,
AUTHOR = {Atiyah, M. F.},
TITLE = {Anniversary address by the {P}resident},
JOURNAL = {Royal Society News},
FJOURNAL = {Royal Society News},
NUMBER = {supplement},
MONTH = {December},
YEAR = {1994},
PAGES = {i--iv, 535--540},
NOTE = {Republished in Atiyah's \textit{Collected
works}, vol.~6. See also version in
\textit{Notes and Records Roy. Soc.
London} \textbf{49}:1 (1995).},
ISSN = {0260-2725},
}
A. Jaffe and F. Quinn :
“Response to comments on ‘Theoretical mathematics’ Bull. Amer. Math. Soc. (N.S.)
30 : 2
(1994 ),
pp. 208–211 .
Response to an article in Bull. Amer. Math. Soc. 30 :2 (1994)
MR
1254077 article
People
BibTeX
@article {key1254077m,
AUTHOR = {Jaffe, Arthur and Quinn, Frank},
TITLE = {Response to comments on ``{T}heoretical
mathematics''},
JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
VOLUME = {30},
NUMBER = {2},
YEAR = {1994},
PAGES = {208--211},
DOI = {10.1090/S0273-0979-1994-00506-3},
NOTE = {Response to an article in \textit{Bull.
Amer. Math. Soc.} \textbf{30}:2 (1994).
MR:1254077.},
ISSN = {0273-0979},
}
M. Atiyah, A. Borel, G. J. Chaitin, D. Friedan, J. Glimm, J. J. Gray, M. W. Hirsch, S. MacLane, B. B. Mandelbrot, D. Ruelle, A. Schwarz, K. Uhlenbeck, R. Thom, E. Witten, and C. Zeeman :
“Responses to ‘Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics’, by A. Jaffe and F. Quinn Bull. Am. Math. Soc., New Ser.
30 : 2
(April 1994 ),
pp. 178–207 .
Zbl
0803.01014 ArXiv
math/9404229 article
Abstract
People
BibTeX
@article {key0803.01014z,
AUTHOR = {Atiyah, Michael and Borel, Armand and
Chaitin, G. J. and Friedan, Daniel and
Glimm, James and Gray, Jeremy J. and
Hirsch, Morris W. and MacLane, Saunders
and Mandelbrot, Benoit B. and Ruelle,
David and Schwarz, Albert and Uhlenbeck,
Karen and Thom, Ren\'e and Witten, Edward
and Zeeman, Christopher},
TITLE = {Responses to ``Theoretical mathematics:
{T}oward a cultural synthesis of mathematics
and theoretical physics'', by {A}.~{J}affe
and {F}.~{Q}uinn},
JOURNAL = {Bull. Am. Math. Soc., New Ser.},
FJOURNAL = {Bulletin of the American Mathematical
Society. New Series},
VOLUME = {30},
NUMBER = {2},
MONTH = {April},
YEAR = {1994},
PAGES = {178--207},
DOI = {10.1090/S0273-0979-1994-00503-8},
NOTE = {ArXiv:math/9404229. Zbl:0803.01014.},
ISSN = {0273-0979},
}
M. Atiyah :
“Contribution to the collected works of Raoul Bott ,”
pp. xxix–xxx
in
Raoul Bott: Collected papers ,
vol. 2: Differential operators .
Edited by R. D. MacPherson .
Contemporary Mathematicians .
Birkhäuser (Boston ),
1994 .
MR
1290365 incollection
People
BibTeX
@incollection {key1290365m,
AUTHOR = {Atiyah, M.},
TITLE = {Contribution to the collected works
of {R}aoul {B}ott},
BOOKTITLE = {Raoul {B}ott: {C}ollected papers},
EDITOR = {MacPherson, R. D.},
VOLUME = {2: Differential operators},
SERIES = {Contemporary Mathematicians},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston},
YEAR = {1994},
PAGES = {xxix--xxx},
NOTE = {MR:1290365.},
ISSN = {0884-7037},
ISBN = {9780817636463},
}
M. Atiyah :
Geometriya i fizika uzlov
[The geometry and physics of knots ].
Mir (Moscow ),
1995 .
Russian translation of The geometry and physics of knots (1990)Miniconference on geometry and physics (1989)
MR
1397266 book
BibTeX
@book {key1397266m,
AUTHOR = {Atiyah, M.},
TITLE = {Geometriya i fizika uzlov [The geometry
and physics of knots]},
PUBLISHER = {Mir},
ADDRESS = {Moscow},
YEAR = {1995},
PAGES = {192},
NOTE = {Russian translation of \textit{The geometry
and physics of knots} (1990). See also
\textit{Miniconference on geometry and
physics} (1989). MR:1397266.},
ISBN = {9785030028927},
}
M. F. Atiyah :
“Book review: ‘Conversations on mind, matter and mathematics’ Times High. Educ. Suppl.
(29 September 1995 ).
Book by Jean-Pierre Changeux and Alain Connes (Princeton University Press, 1995).
Republished in Atiyah’s Collected works , vol. 6 .
article
People
BibTeX
@article {key37504852,
AUTHOR = {Atiyah, M. F.},
TITLE = {Book review: ``{C}onversations on mind,
matter and mathematics''},
JOURNAL = {Times High. Educ. Suppl.},
FJOURNAL = {Times Higher Education Supplement},
MONTH = {29 September},
YEAR = {1995},
URL = {http://www.timeshighereducation.co.uk/161513.article},
NOTE = {Book by Jean-Pierre Changeux and Alain
Connes (Princeton University Press,
1995). Republished in Atiyah's \textit{Collected
works}, vol.~6.},
ISSN = {0049-3929},
}
M. Atiyah :
“Address of the President, Sir Michael Atiyah, O.M., given at the anniversary meeting on 30 November 1994 Notes and Records Roy. Soc. London
49 : 1
(1995 ),
pp. 141–151 .
See also version in Royal Society News (December 1994)
MR
1325201 Zbl
0978.01520 article
BibTeX
@article {key1325201m,
AUTHOR = {Atiyah, Michael},
TITLE = {Address of the {P}resident, {S}ir {M}ichael
{A}tiyah, {O}.{M}., given at the anniversary
meeting on 30 {N}ovember 1994},
JOURNAL = {Notes and Records Roy. Soc. London},
FJOURNAL = {Notes and Records of the Royal Society},
VOLUME = {49},
NUMBER = {1},
YEAR = {1995},
PAGES = {141--151},
DOI = {10.1098/rsnr.1995.0010},
NOTE = {See also version in \textit{Royal Society
News} (December 1994). MR:1325201. Zbl:0978.01520.},
ISSN = {0035-9149},
}
M. Atiyah :
“Reflections on geometry and physics ,”
pp. 1–6
in
Surveys in differential geometry: Proceedings of the conference on geometry and topology
(Cambridge, MA, 23–25 April 1993 ).
Edited by C.-C. Hsiung and S.-T. Yau .
Surveys in differential geometry (Journal of Differential Geometry supplements) 2 .
International Press (Cambridge, MA ),
1995 .
MR
1375254 Zbl
0867.57031 incollection
Abstract
People
BibTeX
I discuss in general terms what has been happening to the theoretical physics/mathematics frontier over the past 15 years. Specifically I refer to the geometric and topological aspects of quantum field theory which have now spread in a variety of directions. New terms such as quantum groups, quantum geometry, quantum cohomology are appearing. These indicate the scope and significance of the interaction, but it is premature in my view to try to force everything into a particular mould. Time will tell what the significant aspects really are and then the right title to adopt will be clearer.
@incollection {key1375254m,
AUTHOR = {Atiyah, Michael},
TITLE = {Reflections on geometry and physics},
BOOKTITLE = {Surveys in differential geometry: {P}roceedings
of the conference on geometry and topology},
EDITOR = {Chuan-Chih Hsiung and Shing-Tung Yau},
SERIES = {Surveys in differential geometry ({J}ournal
of {D}ifferential {G}eometry supplements)},
NUMBER = {2},
PUBLISHER = {International Press},
ADDRESS = {Cambridge, MA},
YEAR = {1995},
PAGES = {1--6},
NOTE = {(Cambridge, MA, 23--25 April 1993).
MR:1375254. Zbl:0867.57031.},
ISSN = {1052-9233},
ISBN = {9781571460271},
}
M. Atiyah :
“The geometry of classical particles ,”
pp. 1–15
in
Proceedings of the conference on geometry and topology held at Harvard University
(Cambridge, MA, 23–25 April 1993 ).
Edited by C.-C. Hsiung and S.-T. Yau .
Surveys in Differential Geometry 2 .
International Press (Somerville, MA ),
1995 .
MR
1919420 Zbl
1050.55502 incollection
People
BibTeX
@incollection {key1919420m,
AUTHOR = {Atiyah, Michael},
TITLE = {The geometry of classical particles},
BOOKTITLE = {Proceedings of the conference on geometry
and topology held at {H}arvard {U}niversity},
EDITOR = {Chuan-Chih Hsiung and Shing-Tung Yau},
SERIES = {Surveys in Differential Geometry},
NUMBER = {2},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {1995},
PAGES = {1--15},
NOTE = {(Cambridge, MA, 23--25 April 1993).
MR:1919420. Zbl:1050.55502.},
ISSN = {1052-9233},
ISBN = {9781571460271},
}
M. Atiyah :
“Reflections on geometry and physics ,”
pp. 423–428
in
Geometry, topology, & physics: Lectures of a conference in honor of Raoul Bott’s 70th birthday
(Harvard University, April 1993 ).
Edited by S.-T. Yau .
Conference proceedings and lecture notes in geometry and topology 4 .
International Press (Cambridge, MA ),
1995 .
MR
1358626 incollection
People
BibTeX
@incollection {key1358626m,
AUTHOR = {Atiyah, Michael},
TITLE = {Reflections on geometry and physics},
BOOKTITLE = {Geometry, topology, \& physics: {L}ectures
of a conference in honor of {R}aoul
{B}ott's 70th birthday},
EDITOR = {Shing-Tung Yau},
SERIES = {Conference proceedings and lecture notes
in geometry and topology},
NUMBER = {4},
PUBLISHER = {International Press},
ADDRESS = {Cambridge, MA},
YEAR = {1995},
PAGES = {423--428},
NOTE = {(Harvard University, April 1993). MR:1358626.},
ISBN = {9781571460240},
}
M. Atiyah :
“Friedrich Hirzebruch: An appreciation ,”
pp. 1–5
in
Proceedings of the Hirzebruch 65 conference on algebraic geometry
(Ramat Gan, Israel, 2–7 May 1993 ).
Edited by M. Teicher .
Israel Mathematical Conference Proceedings 9 .
Bar-Ilan University (Ramat Gan, Israel ),
1996 .
Zbl
0834.01012 incollection
People
BibTeX
@incollection {key0834.01012z,
AUTHOR = {Atiyah, M.},
TITLE = {Friedrich {H}irzebruch: {A}n appreciation},
BOOKTITLE = {Proceedings of the {H}irzebruch 65 conference
on algebraic geometry},
EDITOR = {Teicher, Mina},
SERIES = {Israel Mathematical Conference Proceedings},
NUMBER = {9},
PUBLISHER = {Bar-Ilan University},
ADDRESS = {Ramat Gan, Israel},
YEAR = {1996},
PAGES = {1--5},
NOTE = {(Ramat Gan, Israel, 2--7 May 1993).
Zbl:0834.01012.},
ISSN = {0792-4119},
ISBN = {9789996281068},
}
P. Exner :
“Proofs and physics, their interrelationship ,”
Pokroky Mat. Fyz. Astronom.
41 : 2
(1996 ),
pp. 73–81 .
Adaptation and Czech translation of article from Bull. Amer. Math. Soc. 30 :2 (1994)
MR
1454823 article
People
BibTeX
@article {key1454823m,
AUTHOR = {Pavel Exner},
TITLE = {Proofs and physics, their interrelationship},
JOURNAL = {Pokroky Mat. Fyz. Astronom.},
FJOURNAL = {Pokroky Matematiky, Fysiky a Astronomie},
VOLUME = {41},
NUMBER = {2},
YEAR = {1996},
PAGES = {73--81},
NOTE = {Adaptation and Czech translation of
article from \textit{Bull. Amer. Math.
Soc.} \textbf{30}:2 (1994). MR:1454823.},
ISSN = {0032-2423},
}
M. F. Atiyah :
“The work of Edward Witten ,”
pp. 514–518
in
Fields Medallists’ lectures .
Edited by M. F. Atiyah and D. Iagolnitzer .
World Scientific Series in 20th Century Mathematics 5 .
World Scientific (River Edge, NJ ),
1997 .
MR
1622921 incollection
People
BibTeX
@incollection {key1622921m,
AUTHOR = {Atiyah, Michael F.},
TITLE = {The work of {E}dward {W}itten},
BOOKTITLE = {Fields {M}edallists' lectures},
EDITOR = {Atiyah, Michael F. and Daniel Iagolnitzer},
SERIES = {World Scientific Series in 20th Century
Mathematics},
NUMBER = {5},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {1997},
PAGES = {514--518},
NOTE = {MR:1622921.},
ISBN = {9789810231026},
}
M. F. Atiyah :
“The work of Simon Donaldson ,”
pp. 377–380
in
Fields Medallists’ lectures .
Edited by M. F. Atiyah and D. Iagolnitzer .
World Scientific Series in 20th Century Mathematics 5 .
World Scientific (River Edge, NJ ),
1997 .
MR
1622912 incollection
People
BibTeX
@incollection {key1622912m,
AUTHOR = {Atiyah, Michael F.},
TITLE = {The work of {S}imon {D}onaldson},
BOOKTITLE = {Fields {M}edallists' lectures},
EDITOR = {Atiyah, Michael F. and Daniel Iagolnitzer},
SERIES = {World Scientific Series in 20th Century
Mathematics},
NUMBER = {5},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {1997},
PAGES = {377--380},
NOTE = {MR:1622912.},
ISBN = {9789810231026},
}
M. F. Atiyah :
“An introduction to topological quantum field theories 1–7
in
Proceedings of Gökova geometry-topology conference 1996
(Gökova, Turkey, 27–31 May 1996 ),
published as Turkish J. Math.
21 : 1 .
Issue edited by S. Akbulut, T. Önder, and R. J. Stern .
Scientific and Technological Research Council of Turkey (Ankara ),
1997 .
Republished in Atiyah’s Collected works , vol. 6 .
MR
1456155 Zbl
0890.57019 incollection
People
BibTeX
@article {key1456155m,
AUTHOR = {Atiyah, M. F.},
TITLE = {An introduction to topological quantum
field theories},
JOURNAL = {Turkish J. Math.},
FJOURNAL = {Turkish Journal of Mathematics},
VOLUME = {21},
NUMBER = {1},
YEAR = {1997},
PAGES = {1--7},
URL = {http://journals.tubitak.gov.tr/math/issues/mat-97-21-1/mat-21-1-1-e2101-01.pdf},
NOTE = {\textit{Proceedings of {G}\"okova geometry-topology
conference 1996} (G\"okova, Turkey,
27--31 May 1996). Issue edited by S. Akbulut,
T. \"Onder, and R. J. Stern.
Republished in Atiyah's \textit{Collected
works}, vol.~6. MR:1456155. Zbl:0890.57019.},
ISSN = {1300-0098},
ISBN = {9789754030716},
}
M. F. Atiyah :
“The Dirac equation and geometry ,”
pp. 108–124
in
A. Pais, M. Jacob, D. I. Olive, and M. F. Atiyah :
Paul Dirac: The man and his work .
Edited by P. Goddard .
Cambridge University Press ,
1998 .
MR
1606723 incollection
People
BibTeX
@incollection {key1606723m,
AUTHOR = {Atiyah, Michael F.},
TITLE = {The {D}irac equation and geometry},
BOOKTITLE = {Paul {D}irac: {T}he man and his work},
EDITOR = {Peter Goddard},
PUBLISHER = {Cambridge University Press},
YEAR = {1998},
PAGES = {108--124},
NOTE = {MR:1606723.},
ISBN = {9780521019538},
}
M. Atiyah :
“Roger Penrose: A personal appreciation ,”
pp. 3–7
in
The geometric universe
(Oxford, June 1996 ).
Edited by S. A. Huggett, L. J. Mason, K. P. Tod, S. Tsou, and N. M. J. Woodhouse .
Oxford University Press (New York ),
1998 .
MR
1634501 Zbl
0904.01010 incollection
People
BibTeX
@incollection {key1634501m,
AUTHOR = {Atiyah, Michael},
TITLE = {Roger {P}enrose: {A} personal appreciation},
BOOKTITLE = {The geometric universe},
EDITOR = {S. A. Huggett and Lionel J. Mason and
K. P. Tod and Sheung Tsou and N. M.
J. Woodhouse},
PUBLISHER = {Oxford University Press},
ADDRESS = {New York},
YEAR = {1998},
PAGES = {3--7},
NOTE = {(Oxford, June 1996). MR:1634501. Zbl:0904.01010.},
ISBN = {9780198500599},
}
M. F. Atiyah :
“Obituary: John Arthur Todd Bull. London Math. Soc.
30 : 3
(1998 ),
pp. 305–316 .
MR
1608134 Zbl
0927.01042 article
Abstract
People
BibTeX
John Arthur Todd was one of the last survivors of the school of classical algebraic geometry that flourished in Cambridge under H. F. Baker, FRS. But, unlike most of his contemporaries, with the notable exception of W. V. D. Hodge, FRS, Todd made seminal contributions to the more modern theory, and his name is now enshrined in the literature and widely known.
@article {key1608134m,
AUTHOR = {Atiyah, M. F.},
TITLE = {Obituary: {J}ohn {A}rthur {T}odd},
JOURNAL = {Bull. London Math. Soc.},
FJOURNAL = {Bulletin of the London Mathematical
Society},
VOLUME = {30},
NUMBER = {3},
YEAR = {1998},
PAGES = {305--316},
DOI = {10.1112/S0024609397003871},
NOTE = {MR:1608134. Zbl:0927.01042.},
ISSN = {0024-6093},
}
M. Atiyah :
“Mathematics and the real world ,”
pp. 807–812
in
Current and future challenges in the applications of mathematics ,
published as Quart. Appl. Math.
56 : 4
(1998 ).
MR
1668728 Zbl
1159.00312 incollection
BibTeX
@article {key1668728m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics and the real world},
JOURNAL = {Quart. Appl. Math.},
FJOURNAL = {Quarterly of Applied Mathematics},
VOLUME = {56},
NUMBER = {4},
YEAR = {1998},
PAGES = {807--812},
NOTE = {\textit{Current and future challenges
in the applications of mathematics}.
MR:1668728. Zbl:1159.00312.},
ISSN = {0033-569X},
}
M. Atiyah :
“Mathematics: Queen and servant of the sciences ,”
pp. xxiii–xxvi
in
Sir Michael Atiyah: A great mathematician of the twentieth century ,
published as Asian J. Math.
3 : 1
(1999 ).
Republished from Proc. Am. Phil. Soc. 137 :4 (1993)The founders of index theory (2009)
Zbl
0957.01038 incollection
BibTeX
@article {key0957.01038z,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics: {Q}ueen and servant of
the sciences},
JOURNAL = {Asian J. Math.},
FJOURNAL = {Asian Journal of Mathematics},
VOLUME = {3},
NUMBER = {1},
YEAR = {1999},
PAGES = {xxiii--xxvi},
NOTE = {\textit{Sir {M}ichael {A}tiyah: {A}
great mathematician of the twentieth
century}. Republished from \textit{Proc.
Am. Phil. Soc.} \textbf{137}:4 (1993).
See also \textit{The founders of index
theory} (2009). Zbl:0957.01038.},
ISBN = {9781571460806},
}
M. F. Atiyah :
“Obituary: Kunihiko Kodaira Bull. London Math. Soc.
31 : 4
(1999 ),
pp. 489–493 .
MR
1687532 Zbl
0928.01020 article
People
BibTeX
@article {key1687532m,
AUTHOR = {Atiyah, M. F.},
TITLE = {Obituary: {K}unihiko {K}odaira},
JOURNAL = {Bull. London Math. Soc.},
FJOURNAL = {Bulletin of the London Mathematical
Society},
VOLUME = {31},
NUMBER = {4},
YEAR = {1999},
PAGES = {489--493},
DOI = {10.1112/S0024609398005153},
NOTE = {MR:1687532. Zbl:0928.01020.},
ISSN = {0024-6093},
}
M. Atiyah :
“Geometry and physics in the 20th century ,”
pp. 1–9
in
The mathematical sciences after the year 2000
(Beirut, 11–15 January 1999 ).
Edited by K. Bitar, A. Chamseddine, and W. Sabra .
World Scientific (River Edge, NJ ),
2000 .
MR
1799435 Zbl
0994.01011 incollection
People
BibTeX
@incollection {key1799435m,
AUTHOR = {Atiyah, Michael},
TITLE = {Geometry and physics in the 20th century},
BOOKTITLE = {The mathematical sciences after the
year 2000},
EDITOR = {Bitar, Khalil and Chamseddine, Ali and
Sabra, Wafic},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {2000},
PAGES = {1--9},
NOTE = {(Beirut, 11--15 January 1999). MR:1799435.
Zbl:0994.01011.},
ISBN = {9789810242237},
}
M. F. Atiyah :
“Preface ”
in
Mathematics: Frontiers and perspectives .
Edited by V. Arnold, M. Atiyah, P. Lax, and B. Mazur .
American Mathematical Society (Providence, RI ),
2000 .
Republished in Atiyah’s Collected works , vol. 6 .
incollection
People
BibTeX
@incollection {key89284033,
AUTHOR = {Atiyah, M. F.},
TITLE = {Preface},
BOOKTITLE = {Mathematics: {F}rontiers and perspectives},
EDITOR = {Arnold, V. and Atiyah, M. and Lax, P.
and Mazur, B.},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2000},
NOTE = {Republished in Atiyah's \textit{Collected
works}, vol.~6.},
ISBN = {9780821826973},
}
M. Atiyah :
Equivariant cohomology and representations of the symmetric group .
Preprint ,
2000 .
ArXiv
math/0012215 techreport
Abstract
BibTeX
@techreport {keymath/0012215a,
AUTHOR = {Michael Atiyah},
TITLE = {Equivariant cohomology and representations
of the symmetric group},
TYPE = {Preprint},
YEAR = {2000},
NOTE = {ArXiv:math/0012215.},
}
M. Atiyah :
“Mathematics in the 20th century Amer. Math. Mon.
108 : 7
(2001 ),
pp. 654–666 .
See also versions in Math. Today 37 :2 (2001)Contemporary trends in algebraic geometry and algebraic topology (2002)N.T.M. 10 :1 (2002)Bull. Lond. Math. Soc. 34 :1 (2002)Wiadom. Mat. 39 (2003)Adv. Math. (China) 33 :1 (2004)
MR
1862105 Zbl
1081.01502 article
Abstract
BibTeX
A survey is given of several key themes that have characterised mathematics in the 20th century. The impact of physics is also discussed, and some speculations are made about possible developments in the 21st century. This article is based on the transcript of a recording of the author’s Fields Lecture at the World Mathematical Year 2000 Symposium, Toronto, June 7–9, 2000.
@article {key1862105m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics in the 20th century},
JOURNAL = {Amer. Math. Mon.},
FJOURNAL = {American Mathematical Monthly},
VOLUME = {108},
NUMBER = {7},
YEAR = {2001},
PAGES = {654--666},
DOI = {10.2307/2695275},
NOTE = {See also versions in \textit{Math. Today}
\textbf{37}:2 (2001), \textit{Contemporary
trends in algebraic geometry and algebraic
topology} (2002), \textit{N.T.M.} \textbf{10}:1
(2002), \textit{Bull. Lond. Math. Soc.}
\textbf{34}:1 (2002), \textit{Wiadom.
Mat.} \textbf{39} (2003) and \textit{Adv.
Math. (China)} \textbf{33}:1 (2004).
MR:1862105. Zbl:1081.01502.},
ISSN = {0002-9890},
}
M. Atiyah :
“Mathematics in the 20th century ,”
Math. Today
37 : 2
(2001 ),
pp. 46–53 .
See also versions in Amer. Math. Mon. 108 :7 (2001)Contemporary trends in algebraic geometry and algebraic topology (2002)N.T.M. 10 :1 (2002)Bull. Lond. Math. Soc. 34 :1 (2002)Wiadom. Mat. 39 (2003)Adv. Math. (China) 33 :1 (2004)
MR
1840757 article
Abstract
BibTeX
A survey is given of several key themes that have characterised mathematics in the 20th century. The impact of physics is also discussed, and some speculations are made about possible developments in the 21st century. This article is based on the transcript of a recording of the author’s Fields Lecture at the World Mathematical Year 2000 Symposium, Toronto, June 7–9, 2000.
@article {key1840757m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics in the 20th century},
JOURNAL = {Math. Today},
FJOURNAL = {Mathematics Today -- Bulletin of the
Institute of Mathematics and its Applications},
VOLUME = {37},
NUMBER = {2},
YEAR = {2001},
PAGES = {46--53},
NOTE = {See also versions in \textit{Amer. Math.
Mon.} \textbf{108}:7 (2001), \textit{Contemporary
trends in algebraic geometry and algebraic
topology} (2002), \textit{N.T.M.} \textbf{10}:1
(2002), \textit{Bull. Lond. Math. Soc.}
\textbf{34}:1 (2002), \textit{Wiadom.
Mat.} \textbf{39} (2003) and \textit{Adv.
Math. (China)} \textbf{33}:1 (2004).
MR:1840757.},
ISSN = {1361-2042},
}
M. Atiyah, J. Maldacena, and C. Vafa :
“An M-theory flop as a large \( N \) duality J. Math. Phys.
42 : 7
(2001 ),
pp. 3209–3220 .
MR
1840340 Zbl
1061.81056 article
Abstract
People
BibTeX
@article {key1840340m,
AUTHOR = {Atiyah, Michael and Maldacena, Juan
and Vafa, Cumrun},
TITLE = {An {M}-theory flop as a large \$N\$ duality},
JOURNAL = {J. Math. Phys.},
FJOURNAL = {Journal of Mathematical Physics},
VOLUME = {42},
NUMBER = {7},
YEAR = {2001},
PAGES = {3209--3220},
DOI = {10.1063/1.1376159},
NOTE = {MR:1840340. Zbl:1061.81056.},
ISSN = {0022-2488},
}
M. Atiyah :
“Configurations of points 1375–1387
in
Topological methods in the physical sciences
(London, 2000 ),
published as R. Soc. Lond. Philos. Trans. Ser. A
359 : 1784
(July 2001 ).
MR
1853626 Zbl
1037.58007 incollection
Abstract
BibTeX
Berry & Robbins, in their discussion of the spin-statistics theorem in quantum mechanics, were led to ask the following question. Can one construct a continuous map from the configuration space of \( n \) distinct particles in 3-space to the flag manifold of the unitary group \( U(n) \) ? I shall discuss this problem and various generalizations of it. In particular, there is a version in which \( U(n) \) is replaced by an arbitrary compact Lie group. It turns out that this can be treated using Nahm’s equations, which are an integrable system of ordinary differential equations arising from the self-dual Yang–Mills equations. Our topological problem is therefore connected with physics in two quite different ways, once at its origin and once at its solution.
@article {key1853626m,
AUTHOR = {Atiyah, Michael},
TITLE = {Configurations of points},
JOURNAL = {R. Soc. Lond. Philos. Trans. Ser. A},
FJOURNAL = {Philosophical Transactions of the Royal
Society A: Mathematical, Physical \&
Engineering Sciences},
VOLUME = {359},
NUMBER = {1784},
MONTH = {July},
YEAR = {2001},
PAGES = {1375--1387},
DOI = {10.1098/rsta.2001.0840},
NOTE = {\textit{Topological methods in the physical
sciences} (London, 2000). MR:1853626.
Zbl:1037.58007.},
ISSN = {1364-503X},
}
M. Atiyah :
“Equivariant cohomology and representations of the symmetric group Chinese Ann. Math. Ser. B
22 : 1
(2001 ),
pp. 23–30 .
MR
1823127 Zbl
1057.20007 article
Abstract
BibTeX
In a recent paper the author constructed a continuous map from the configuration space of \( n \) distinct ordered points in 3-space to the flag manifold of the unitary group \( U(n) \) , which is compatible with the action of the symmetric group. This map is also compatible with appropriate actions of the rotation group \( \mathit{SO}(3) \) . In this paper the author studies the induced homomorphism in \( \mathit{SO}(3) \) -equivariant cohomology and shows that this contains much interesting information involving representations of the symmetric group.
@article {key1823127m,
AUTHOR = {Atiyah, M.},
TITLE = {Equivariant cohomology and representations
of the symmetric group},
JOURNAL = {Chinese Ann. Math. Ser. B},
FJOURNAL = {Chinese Annals of Mathematics, Series
B},
VOLUME = {22},
NUMBER = {1},
YEAR = {2001},
PAGES = {23--30},
DOI = {10.1142/S0252959901000048},
NOTE = {MR:1823127. Zbl:1057.20007.},
ISSN = {0252-9599},
}
M. Atiyah :
“\( K \) -theory past and present411–417
in
Sitzungsberichte der Berliner Mathematischen Gesellschaft, 1997–2000 .
Berliner Mathematischen Gesellschaft ,
2001 .
MR
2091892 Zbl
1061.19500 ArXiv
math/0012213 incollection
Abstract
People
BibTeX
@incollection {key2091892m,
AUTHOR = {Atiyah, Michael},
TITLE = {\$K\$-theory past and present},
BOOKTITLE = {Sitzungsberichte der {B}erliner {M}athematischen
{G}esellschaft, 1997--2000},
PUBLISHER = {Berliner Mathematischen Gesellschaft},
YEAR = {2001},
PAGES = {411--417},
NOTE = {ArXiv:math/0012213. MR:2091892. Zbl:1061.19500.},
}
M. Atiyah :
“Mathematics in the 20th century 1–21
in
Contemporary trends in algebraic geometry and algebraic topology
(Tianjin, China, 9–13 October 2000 ).
Edited by S.-S. Chern, L. Fu, and R. M. Hain .
Nankai Tracts in Mathematics 5 .
World Scientific (River Edge, NJ ),
2002 .
See also versions in Amer. Math. Mon. 108 :7 (2001)Math. Today 37 :2 (2001)N.T.M. 10 :1 (2002)Bull. Lond. Math. Soc. 34 :1 (2002)Wiadom. Mat. 39 (2003)Adv. Math. (China) 33 :1 (2004)
MR
1945353 Zbl
1038.01014 incollection
Abstract
People
BibTeX
A survey is given of several key themes that have characterised mathematics in the 20th century. The impact of physics is also discussed, and some speculations are made about possible developments in the 21st century. This article is based on the transcript of a recording of the author’s Fields Lecture at the World Mathematical Year 2000 Symposium, Toronto, June 7–9, 2000.
@incollection {key1945353m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics in the 20th century},
BOOKTITLE = {Contemporary trends in algebraic geometry
and algebraic topology},
EDITOR = {Shiing-Shen Chern and Lei Fu and Richard
Martin Hain},
SERIES = {Nankai Tracts in Mathematics},
NUMBER = {5},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {2002},
PAGES = {1--21},
DOI = {10.1142/9789812777416_0001},
NOTE = {(Tianjin, China, 9--13 October 2000).
See also versions in \textit{Amer. Math.
Mon.} \textbf{108}:7 (2001), \textit{Math.
Today} \textbf{37}:2 (2001), \textit{N.T.M.}
\textbf{10}:1 (2002), \textit{Bull.
Lond. Math. Soc.} \textbf{34}:1 (2002),
\textit{Wiadom. Mat.} \textbf{39} (2003)
and \textit{Adv. Math. (China)} \textbf{33}:1
(2004). MR:1945353. Zbl:1038.01014.},
ISBN = {9789810249540},
}
M. Atiyah :
“Mathematics in the 20th century Bull. Lond. Math. Soc.
34 : 1
(2002 ),
pp. 1–15 .
See also versions in Amer. Math. Mon. 108 :7 (2001)Math. Today 37 :2 (2001)Contemporary trends in algebraic geometry and algebraic topology (2002)N.T.M. 10 :1 (2002)Wiadom. Mat. 39 (2003)Adv. Math. (China) 33 :1 (2004)
MR
1866422 Zbl
1022.01007 article
Abstract
BibTeX
A survey is given of several key themes that have characterised mathematics in the 20th century. The impact of physics is also discussed, and some speculations are made about possible developments in the 21st century. This article is based on the transcript of a recording of the author’s Fields Lecture at the World Mathematical Year 2000 Symposium, Toronto, June 7–9, 2000.
@article {key1866422m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics in the 20th century},
JOURNAL = {Bull. Lond. Math. Soc.},
FJOURNAL = {Bulletin of the London Mathematical
Society},
VOLUME = {34},
NUMBER = {1},
YEAR = {2002},
PAGES = {1--15},
DOI = {10.1112/S0024609301008566},
NOTE = {See also versions in \textit{Amer. Math.
Mon.} \textbf{108}:7 (2001), \textit{Math.
Today} \textbf{37}:2 (2001), \textit{Contemporary
trends in algebraic geometry and algebraic
topology} (2002), \textit{N.T.M.} \textbf{10}:1
(2002), \textit{Wiadom. Mat.} \textbf{39}
(2003), \textit{Adv. Math. (China)}
\textbf{33}:1 (2004). MR:1866422. Zbl:1022.01007.},
ISSN = {0024-6093},
}
M. Atiyah and P. Sutcliffe :
“The geometry of point particles R. Soc. Lond. Proc. Ser. A
458 : 2021
(2002 ),
pp. 1089–1115 .
MR
1902577 Zbl
1010.58015 article
Abstract
People
BibTeX
There is a very natural map from the configuration space of \( n \) distinct points in Euclidean 3-space into the flag manifold \( U(n)/U(1)^n \) , which is compatible with the action of the symmetric group. The map is well defined for all configurations of points provided a certain conjecture holds, for which we provide numerical evidence. We propose some additional conjectures, which imply the first, and test these numerically. Motivated by the above map, we define a geometrical multi-particle energy function and compute the energy-minimizing configurations for up to 32 particles. These configurations comprise the vertices of polyhedral structures that are dual to those found in a number of complicated physical theories, such as Skyrmions and fullerenes. Comparisons with 2- and 3-particle energy functions are made. The planar restriction and the generalization to hyperbolic 3-space are also investigated.
@article {key1902577m,
AUTHOR = {Atiyah, Michael and Sutcliffe, Paul},
TITLE = {The geometry of point particles},
JOURNAL = {R. Soc. Lond. Proc. Ser. A},
FJOURNAL = {Proceedings of the Royal Society A:
Mathematical, Physical \& Engineering
Sciences},
VOLUME = {458},
NUMBER = {2021},
YEAR = {2002},
PAGES = {1089--1115},
DOI = {10.1098/rspa.2001.0913},
NOTE = {MR:1902577. Zbl:1010.58015.},
ISSN = {1364-5021},
}
M. Atiyah :
“Mathematics in the 20th century N.T.M. (N.S.)
10 : 1
(2002 ),
pp. 25–39 .
See also versions in Amer. Math. Mon. 108 :7 (2001)Math. Today 37 :2 (2001)Contemporary trends in algebraic geometry and algebraic topology (2002)Bull. Lond. Math. Soc. 34 :1 (2002)Wiadom. Mat. 39 (2003)Adv. Math. (China) 33 :1 (2004)
MR
1894494 Zbl
0991.01015 article
Abstract
BibTeX
A survey is given of several key themes that have characterised mathematics in the 20th century. The impact of physics is also discussed, and some speculations are made about possible developments in the 21st century. This article is based on the transcript of a recording of the author’s Fields Lecture at the World Mathematical Year 2000 Symposium, Toronto, June 7–9, 2000.
@article {key1894494m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics in the 20th century},
JOURNAL = {N.T.M. (N.S.)},
FJOURNAL = {NTM International Journal of History
and Ethics of Natural Sciences, Technology
and Medicine, new series},
VOLUME = {10},
NUMBER = {1},
YEAR = {2002},
PAGES = {25--39},
DOI = {10.1007/BF03033096},
NOTE = {See also versions in \textit{Amer. Math.
Mon.} \textbf{108}:7 (2001), \textit{Math.
Today} \textbf{37}:2 (2001), \textit{Contemporary
trends in algebraic geometry and algebraic
topology} (2002), \textit{Bull. Lond.
Math. Soc.} \textbf{34}:1 (2002), \textit{Wiadom.
Mat.} \textbf{39} (2003) and \textit{Adv.
Math. (China)} \textbf{33}:1 (2004).
MR:1894494. Zbl:0991.01015.},
ISSN = {0036-6978},
}
M. F. Atiyah :
“Hermann Weyl: 1885–1955 Biog. Mem. Nat. Acad. Sci.
82
(2002 ),
pp. 3–17 .
Republished in Atiyah’s Collected works , vol. 6 .
article
People
BibTeX
@article {key25115447,
AUTHOR = {Atiyah, M. F.},
TITLE = {Hermann {W}eyl: 1885--1955},
JOURNAL = {Biog. Mem. Nat. Acad. Sci.},
FJOURNAL = {Biographical Memoirs of the National
Academy of Sciences},
VOLUME = {82},
YEAR = {2002},
PAGES = {3--17},
URL = {http://www.nap.edu/html/biomems/hweyl.pdf},
NOTE = {Republished in Atiyah's \textit{Collected
works}, vol.~6.},
ISSN = {0077-2933},
}
M. Atiyah and E. Witten :
“\( M \) -theory dynamics on a manifold of \( G_2 \) holonomyAdv. Theor. Math. Phys.
6 : 1
(2002 ),
pp. 1–106 .
MR
1992874 Zbl
1033.81065 article
Abstract
People
BibTeX
We analyze the dynamics of \( M \) -theory on a manifold of \( G_2 \) holonomy that is developing a conical singularity. The known cases involve a cone on \( \mathbb{CP}^3 \) , where we argue that the dynamics involves restoration of a global symmetry, \( \mathit{SU}(3)/U(1)^2 \) , where we argue that there are phase transitions among three possible branches corresponding to three classical spacetimes, and \( S^3 \times S^3 \) and its quotients, where we recover and extend previous results about smooth continuations between different spacetimes and relations to four-dimensional gauge theory.
@article {key1992874m,
AUTHOR = {Atiyah, Michael and Witten, Edward},
TITLE = {\$M\$-theory dynamics on a manifold of
\$G_2\$ holonomy},
JOURNAL = {Adv. Theor. Math. Phys.},
FJOURNAL = {Advances in Theoretical and Mathematical
Physics},
VOLUME = {6},
NUMBER = {1},
YEAR = {2002},
PAGES = {1--106},
NOTE = {MR:1992874. Zbl:1033.81065.},
ISSN = {1095-0761},
}
M. Atiyah and R. Bielawski :
“Nahm’s equations, configuration spaces and flag manifolds Bull. Braz. Math. Soc. (N.S.)
33 : 2
(2002 ),
pp. 157–176 .
MR
1940347 Zbl
1022.22007 ArXiv
math/0110112 article
Abstract
People
BibTeX
We give a positive answer to the Berry–Robbins problem for any compact Lie group \( G \) , i.e. we show the existence of a smooth \( W \) -equivariant map from the space of regular triples in a Cartan subalgebra to the flag manifold \( G/T \) . This map is constructed via solutions to Nahm’s equations and it is compatible with the \( \mathit{SO}(3) \) action, where \( \mathit{SO}(3) \) acts on \( G/T \) via a regular homomorphism from \( \mathit{SU}(2) \) to \( G \) . We then generalize this picture to include an arbitrary homomorphism from \( \mathit{SU}(2) \) to \( G \) . This leads to an interesting geometrical picture which appears to be related to the Springer representation of the Weyl group and the work of Kazhdan and Lusztig on representations of Hecke algebras.
@article {key1940347m,
AUTHOR = {Atiyah, Michael and Bielawski, Roger},
TITLE = {Nahm's equations, configuration spaces
and flag manifolds},
JOURNAL = {Bull. Braz. Math. Soc. (N.S.)},
FJOURNAL = {Bulletin of the Brazilian Mathematical
Society, new series},
VOLUME = {33},
NUMBER = {2},
YEAR = {2002},
PAGES = {157--176},
DOI = {10.1007/s005740200007},
NOTE = {ArXiv:math/0110112. MR:1940347. Zbl:1022.22007.},
ISSN = {1678-7544},
}
M. Atiyah :
“Mathematics in the 20th century ,”
Wiadom. Mat.
39
(2003 ),
pp. 47–63 .
Polish translation of Bull. Lond. Math. Soc. 34 :1 (2002)Amer. Math. Mon. 108 :7 (2001)Math. Today 37 :2 (2001)Contemporary trends in algebraic geometry and algebraic topology (2002)N.T.M. 10 :1 (2002)Adv. Math. (China) 33 :1 (2004)
MR
2043772 article
Abstract
BibTeX
A survey is given of several key themes that have characterised mathematics in the 20th century. The impact of physics is also discussed, and some speculations are made about possible developments in the 21st century. This article is based on the transcript of a recording of the author’s Fields Lecture at the World Mathematical Year 2000 Symposium, Toronto, June 7–9, 2000.
@article {key2043772m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics in the 20th century},
JOURNAL = {Wiadom. Mat.},
FJOURNAL = {Wiadomo\'sci Matematyczne},
VOLUME = {39},
YEAR = {2003},
PAGES = {47--63},
NOTE = {Polish translation of \textit{Bull.
Lond. Math. Soc.} \textbf{34}:1 (2002).
See also versions in \textit{Amer. Math.
Mon.} \textbf{108}:7 (2001), \textit{Math.
Today} \textbf{37}:2 (2001), \textit{Contemporary
trends in algebraic geometry and algebraic
topology} (2002), \textit{N.T.M.} \textbf{10}:1
(2002) and \textit{Adv. Math. (China)}
\textbf{33}:1 (2004). MR:2043772.},
ISSN = {0373-8302},
}
M. Atiyah and J. Berndt :
“Projective planes, Severi varieties and spheres ,”
pp. 1–27
in
Surveys in differential geometry: Lectures on geometry and topology held in honor of Calabi, Lawson, Siu, and Uhlenbeck
(Harvard University, 3–5 May 2002 ).
Edited by S.-T. Yau .
Surveys in Differential Geometry (Journal of Differential Geometry supplements) 8 .
International Press (Somerville, MA ),
2003 .
MR
2039984 Zbl
1057.53040 ArXiv
math/0206135 incollection
Abstract
People
BibTeX
@incollection {key2039984m,
AUTHOR = {Atiyah, Michael and Berndt, J{\"u}rgen},
TITLE = {Projective planes, {S}everi varieties
and spheres},
BOOKTITLE = {Surveys in differential geometry: {L}ectures
on geometry and topology held in honor
of {C}alabi, {L}awson, {S}iu, and {U}hlenbeck},
EDITOR = {Shing-Tung Yau},
SERIES = {Surveys in Differential Geometry ({J}ournal
of {D}ifferential {G}eometry supplements)},
NUMBER = {8},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2003},
PAGES = {1--27},
NOTE = {(Harvard University, 3--5 May 2002).
ArXiv:math/0206135. MR:2039984. Zbl:1057.53040.},
ISSN = {1052-9233},
ISBN = {9781571461148},
}
M. Atiyah and P. Sutcliffe :
“Polyhedra in physics, chemistry and geometry Milan J. Math.
71 : 1
(2003 ),
pp. 33–58 .
MR
2120915 Zbl
1050.52002 article
Abstract
People
BibTeX
In this article we review some problems in physics, chemistry and mathematics that lead naturally to a class of polyhedra which include the Platonic solids. Examples include the study of electrons on a sphere, cages of carbon atoms, central configurations of gravitating point particles, rare gas microclusters, soliton models of nuclei, magnetic monopole scattering and geometrical problems concerning point particles.
@article {key2120915m,
AUTHOR = {Atiyah, Michael and Sutcliffe, Paul},
TITLE = {Polyhedra in physics, chemistry and
geometry},
JOURNAL = {Milan J. Math.},
FJOURNAL = {Milan Journal of Mathematics},
VOLUME = {71},
NUMBER = {1},
YEAR = {2003},
PAGES = {33--58},
DOI = {10.1007/s00032-003-0014-1},
NOTE = {MR:2120915. Zbl:1050.52002.},
ISSN = {1424-9286},
}
The founders of index theory: Reminiscences of Atiyah, Bott, Hirzebruch, and Singer .
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2003 .
Republished in 2009 .
MR
2136846 Zbl
1072.01021 book
People
BibTeX
@book {key2136846m,
TITLE = {The founders of index theory: {R}eminiscences
of {A}tiyah, {B}ott, {H}irzebruch, and
{S}inger},
EDITOR = {Yau, S.-T.},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2003},
PAGES = {liv+358},
NOTE = {Republished in 2009. MR:2136846. Zbl:1072.01021.},
ISBN = {9781571461209},
}
M. Atiyah :
Collected works ,
vol. 6 .
Oxford Science Publications .
The Clarendon Press and Oxford University Press (Oxford, New York ),
2004 .
MR
2160826 Zbl
1099.01024 book
BibTeX
@book {key2160826m,
AUTHOR = {Atiyah, Michael},
TITLE = {Collected works},
VOLUME = {6},
SERIES = {Oxford Science Publications},
PUBLISHER = {The Clarendon Press and Oxford University
Press},
ADDRESS = {Oxford, New York},
YEAR = {2004},
PAGES = {xxv+1030},
NOTE = {MR:2160826. Zbl:1099.01024.},
ISBN = {9780198530992},
}
M. Atiyah and M. Hopkins :
“A variant of \( K \) -theory: \( K_\pm \) 5–17
in
Topology, geometry and quantum field theory
(Oxford, 24–29 June 2002 ).
Edited by U. Tillmann .
Cambridge University Press ,
2004 .
MR
2079369 Zbl
1090.19004 incollection
Abstract
People
BibTeX
Topological \( K \) -theory has many variants which have been developed and exploited for geometric purposes. There are real or quaternionic versions, “real” \( K \) -theory in the sense of, equivariant \( K \) -theory and combinations of all these.
In recent years \( K \) -theory has found unexpected application in the physics of string theories and all variants of \( K \) -theory that had previously been developed appear to be needed. There are even variants, needed for the physics, which had previously escaped attention, and it is one such variant that is the subject of this paper.
This variant, denoted by \( K_{\pm}(X) \) , was introduced by Witten in relation to “orientifolds”. The geometric situation concerns a manifold \( X \) with an involution \( \tau \) having a fixed sub-manifold \( Y \) . On \( X \) one wants to study a pair of complex vector bundles \( (E^+, E^-) \) with the property that \( \tau \) interchanges them. If we think of the virtual vector bundle \( E^+ - E^- \) , then \( \tau \) takes this into its negative, and \( K_{\pm}(X) \) is meant to be the appropriate K-theory of this situation.
In physics, \( X \) is a 10-dimensional Lorentzian manifold and maps \( \Sigma \to X \) of a surface \( \Sigma \) describe the world-sheet of strings. The symmetry requirements for the appropriate Feynman integral impose conditions that the putative \( K \) -theory \( K_{\pm}(X) \) has to satisfy.
The second author proposed a precise topological definition of \( K_{\pm}(X) \) which appears to meet the physics requirements, but it was not entirely clear how to link the physics with the geometry.
@incollection {key2079369m,
AUTHOR = {Atiyah, Michael and Hopkins, Michael},
TITLE = {A variant of \$K\$-theory: \$K_\pm\$},
BOOKTITLE = {Topology, geometry and quantum field
theory},
EDITOR = {Tillmann, Ulrike},
PUBLISHER = {Cambridge University Press},
YEAR = {2004},
PAGES = {5--17},
DOI = {10.1017/CBO9780511526398.004},
NOTE = {(Oxford, 24--29 June 2002). MR:2079369.
Zbl:1090.19004.},
ISBN = {9780521540490},
}
M. F. Atiyah :
“The geometry and physics of knots ,”
pp. 289–304
in
Collected works ,
vol. 6 .
Oxford Science Publications .
Clarendon Press and Oxford University Press (Oxford, New York ),
2004 .
See also Miniconference on geometry and physics (1989)1990 book of the same title and the Russian translation Geometriya i fizika uzlov (1995)
incollection
BibTeX
@incollection {key57679448,
AUTHOR = {Atiyah, M. F.},
TITLE = {The geometry and physics of knots},
BOOKTITLE = {Collected works},
VOLUME = {6},
SERIES = {Oxford Science Publications},
PUBLISHER = {Clarendon Press and Oxford University
Press},
ADDRESS = {Oxford, New York},
YEAR = {2004},
PAGES = {289--304},
NOTE = {See also \textit{Miniconference on geometry
and physics} (1989), the 1990 book of
the same title and the Russian translation
\textit{Geometriya i fizika uzlov} (1995).},
ISBN = {9780198530992},
}
M. Atiyah :
“Mathematics in the 20th century ,”
Adv. Math. (China)
33 : 1
(2004 ),
pp. 26–40 .
See also versions in Amer. Math. Mon. 108 :7 (2001)Math. Today 37 :2 (2001)Contemporary trends in algebraic geometry and algebraic topology (2002)N.T.M. 10 :1 (2002)Bull. Lond. Math. Soc. 34 :1 (2002)Wiadom. Mat. 39 (2003)
MR
2058440 article
Abstract
BibTeX
A survey is given of several key themes that have characterised mathematics in the 20th century. The impact of physics is also discussed, and some speculations are made about possible developments in the 21st century. This article is based on the transcript of a recording of the author’s Fields Lecture at the World Mathematical Year 2000 Symposium, Toronto, June 7–9, 2000.
@article {key2058440m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics in the 20th century},
JOURNAL = {Adv. Math. (China)},
FJOURNAL = {Advances in Mathematics (China)},
VOLUME = {33},
NUMBER = {1},
YEAR = {2004},
PAGES = {26--40},
NOTE = {See also versions in \textit{Amer. Math.
Mon.} \textbf{108}:7 (2001), \textit{Math.
Today} \textbf{37}:2 (2001), \textit{Contemporary
trends in algebraic geometry and algebraic
topology} (2002), \textit{N.T.M.} \textbf{10}:1
(2002), \textit{Bull. Lond. Math. Soc.}
\textbf{34}:1 (2002) and \textit{Wiadom.
Mat.} \textbf{39} (2003). MR:2058440.},
ISSN = {1000-0917},
}
M. Atiyah and G. Segal :
“Twisted \( K \) -theory ,”
Ukr. Mat. Visn.
1 : 3
(2004 ),
pp. 287–330 .
MR
2172633 Zbl
1151.55301 article
People
BibTeX
@article {key2172633m,
AUTHOR = {Atiyah, Michael and Segal, Graeme},
TITLE = {Twisted \$K\$-theory},
JOURNAL = {Ukr. Mat. Visn.},
FJOURNAL = {Ukra\"ins'kyj Matematychnyj Visnyk},
VOLUME = {1},
NUMBER = {3},
YEAR = {2004},
PAGES = {287--330},
NOTE = {MR:2172633. Zbl:1151.55301.},
ISSN = {1810-3200},
}
M. Atiyah :
“The interaction between geometry and physics ,”
pp. 1–15
in
The unity of mathematics
(Cambridge, MA, 31 August–4 September 2003 ).
Edited by P. I. Ètingof, V. Retakh, and I. M. Singer .
Progress in Mathematics 244 .
Birkhäuser (Boston, MA ),
2006 .
MR
2181802 Zbl
1118.58002 incollection
People
BibTeX
@incollection {key2181802m,
AUTHOR = {Atiyah, Michael},
TITLE = {The interaction between geometry and
physics},
BOOKTITLE = {The unity of mathematics},
EDITOR = {Pavel I. \`Etingof and Vladimir Retakh
and Isadore Manuel Singer},
SERIES = {Progress in Mathematics},
NUMBER = {244},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston, MA},
YEAR = {2006},
PAGES = {1--15},
NOTE = {(Cambridge, MA, 31 August--4 September
2003). MR:2181802. Zbl:1118.58002.},
ISSN = {0743-1643},
ISBN = {9780817640767},
}
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Republication of 2003 original .
MR
2547480 Zbl
1195.01090 book
People
BibTeX
@book {key2547480m,
TITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. Singer},
EDITOR = {Yau, S.-T.},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {lii+393},
NOTE = {Republication of 2003 original. MR:2547480.
Zbl:1195.01090.},
ISBN = {9781571461377},
}
M. F. Atiyah :
“A personal history ,”
pp. 5–15
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Republished in Atiyah’s Collected works , vol. 6 .
incollection
People
BibTeX
@incollection {key72270854,
AUTHOR = {Atiyah, M. F.},
TITLE = {A personal history},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {5--15},
NOTE = {Republished in Atiyah's \textit{Collected
works}, vol.~6.},
ISBN = {9781571461377},
}
