Michael Atiyah | Academic Influence

Why Is Michael Atiyah Influential?

According to Wikipedia, Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004. Life Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at the University of Oxford and the University of Cambridge and in the United States at the Institute for Advanced Study. He was the President of the Royal Society , founding director of the Isaac Newton Institute , master of Trinity College, Cambridge , chancellor of the University of Leicester , and the President of the Royal Society of Edinburgh . From 1997 until his death, he was an honorary professor in the University of Edinburgh.

Michael Atiyah's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

Introduction to commutative algebra (1969) (3782)
The Yang-Mills equations over Riemann surfaces (1983) (1942)
Self-duality in four-dimensional Riemannian geometry (1978) (1338)
Construction of Instantons (1978) (1190)
Spectral Asymmetry and Riemannian Geometry (1973) (1143)
The moment map and equivariant cohomology (1984) (1069)
The Index of elliptic operators. 1 (1968) (964)
Spectral asymmetry and Riemannian geometry I (1975) (933)
The Index of elliptic operators. 3. (1968) (920)
Convexity and Commuting Hamiltonians (1982) (866)
Vector Bundles Over an Elliptic Curve (1957) (845)
The Geometry and Dynamics of Magnetic Monopoles (1988) (820)
Complex analytic connections in fibre bundles (1957) (777)
The Index of Elliptic Operators: IV (1971) (759)
THE INDEX OF ELLIPTIC OPERATORS (1997) (625)
Spectral asymmetry and Riemannian geometry. II (2007) (619)
Topological quantum field theories (1988) (593)
A Lefschetz Fixed Point Formula for Elliptic Complexes: I (1967) (565)
Vector bundles and homogeneous spaces (1961) (540)
The index of elliptic operators on compact manifolds (1963) (520)
On the heat equation and the index theorem (1973) (503)
Seminar on the Atiyah-Singer Index Theorem. (1968) (486)
The Index of Elliptic Operators: II (1968) (469)
Elliptic operators, discrete groups and von Neumann algebras (1976) (465)
The Index of elliptic operators. 5. (1971) (441)
A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications (1968) (405)
Instantons and algebraic geometry (1977) (391)
Equivariant $K$-theory and completion (1969) (383)
M-Theory Dynamics On A Manifold Of G_2 Holonomy (2001) (357)
Characters and cohomology of finite groups (1961) (349)
Dirac operators coupled to vector potentials. (1984) (346)
K -THEORY AND REALITY (1966) (338)
Resolution of Singularities and Division of Distributions (1970) (316)
Riemann surfaces and spin structures (1971) (305)
Index theory for skew-adjoint fredholm operators (1969) (291)
Elliptic operators and compact groups (1974) (282)
The geometry and physics of knots: Frontmatter (1990) (262)
Twisted K-theory (2004) (255)
Lacunas for hyperbolic differential operators with constant coefficients I (1970) (246)
An M theory flop as a large N duality (2001) (226)
BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS (1968) (222)
Spin-manifolds and group actions (1970) (217)
On the Krull-Schmidt theorem with application to sheaves (1956) (209)
Low energy scattering of non-Abelian monopoles (1985) (204)
Group representations, λ-rings and the J-homomorphism (1969) (195)
Topological aspects of Yang-Mills theory (1978) (193)
The Geometry and Physics of Knots (1990) (187)
Analytic cycles on complex manifolds (1962) (186)
Skyrmions from instantons (1989) (173)
Mathematics: Frontiers and Perspectives (2000) (160)
Riemann-Roch theorems for differentiable manifolds (1959) (157)
On the heat equation and the index theorem (1973) (156)
The experience of mathematical beauty and its neural correlates (2014) (153)
POWER OPERATIONS IN K -THEORY (1966) (140)
On framings of 3-manifolds (1990) (140)
Instantons in two and four dimensions (1984) (138)
Topological Lagrangians and cohomology (1990) (131)
On equivariant Euler characteristics (1989) (131)
The logarithm of the dedekind η-function (1987) (128)
On analytic surfaces with double points (1958) (127)
Twisted K-theory and cohomology (2005) (119)
Bordism and Cobordism (1961) (109)
The Index Problem for Manifolds with Boundary (1994) (107)
SYMMETRIES OF ISLAMIC GEOMETRICAL PATTERNS (1994) (102)
Lie theory and geometry : in honor of Bertram Kostant (1997) (100)
A geometric construction of the discrete series for semisimple Lie groups (1977) (98)
Circular symmetry and stationary phase approximation (1981) (94)
On the periodicity theorem for complex vector bundles (1964) (89)
Vector bundles and the Künneth formula (1962) (87)
K -THEORY AND THE HOPF INVARIANT (1966) (86)
A Geometric Construction of the Discrete Series for Semisimple Lie Groups (2005) (86)
Sir Michael Atiyah : a great mathematician of the twentieth century (1999) (82)
New invariants of 3 and 4 dimensional manifolds (1987) (82)
Deformations of instantons. (1977) (79)
THE GEOMETRY AND DYNAMICS OF MAGNETIC MONOPOLES. M.B. PORTER LECTURES (1988) (78)
Geometry and kinematics of two Skyrmions (1993) (75)
Eta invariants, signature defects of cusps, and values of L-functions (1983) (74)
A Lefschetz fixed point formula for elliptic differential operators (1966) (72)
Low-energy scattering of non-Abelian magnetic monopoles (1985) (72)
Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn (1994) (70)
Notes on the Lefschetz fixed point theorem for elliptic complexes (1964) (70)
Polyhedra in Physics, Chemistry and Geometry (2003) (70)
Complex Fibre Bundles and Ruled Surfaces (1955) (67)
Introduction to the Problem of Minimal Models in the Theory of Algebraic Surfaces (1960) (66)
Integrals of the Second Kind on an Algebraic Variety (1955) (65)
The geometry of point particles (2002) (64)
The Riemann–Roch theorem for analytic embeddings (1962) (59)
Vector fields with finite singularities (1972) (55)
The Nature of Mathematical Proof (2005) (52)
Topological quantum field theory (2003) (52)
Angular momentum, convex Polyhedra and Algebraic Geometry (1983) (52)
Topological quantum field theory (2003) (52)
Vector bundles on projective 3-space (1976) (52)
Vector Fields on Manifolds (1970) (50)
Immersions and embeddings of manifolds (1962) (47)
Geometry and physics (2010) (47)
Twistor theory at fifty: from contour integrals to twistor strings (2017) (47)
The Unity of Mathematics (1978) (46)
Representation Theory of Lie Groups (1980) (44)
On complex Stiefel manifolds (1960) (43)
The signature of fibre-bundles (2015) (42)
Curvature, cones and characteristic numbers (2013) (41)
On the K-theory of compact lie groups (1965) (41)
Mathematics in the 20th Century (2001) (41)
Responses to: A. Jaffe and F. Quinn, “Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics” [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1–13; MR1202292 (94h:00007)] (1994) (40)
Compact lie groups and the stable homotopy of spheres (1974) (40)
Eigenvalues of the dirac operator (1985) (40)
Convexity and Loop Groups (1983) (38)
Algebraic topology and operators in Hilbert space (1969) (37)
Geometric models of matter (2012) (35)
Projective planes, Severi varieties and spheres (2002) (34)
Quantum theory and geometry (1995) (33)
Configurations of points (2001) (33)
Nahm’s equations, configuration spaces and flag manifolds (2001) (32)
K-Theory Past and Present (2000) (32)
The geometry of classical particles (2002) (31)
Bott Periodicity and the Parallelizability of the spheres (1961) (30)
Mathematics for physics (1983) (29)
Idempotency: List of Participants (1998) (29)
The Art of Mathematics (2009) (29)
Bakerian Lecture, 1975: Global geometry (1976) (26)
Skyrmions, instantons, mass and curvature (2005) (23)
X-THEORY AND REALITY (1966) (23)
Lacunas for hyperbolic differential operators with constant coefficients. II (1973) (23)
NEW INVARIANTS OF THREE-DIMENSIONAL AND FOUR-DIMENSIONAL MANIFOLDS (1987) (22)
Mathematics in the 20th century (2002) (21)
A Variant of K-theory: K_{+-} (2003) (21)
EXPONENTIAL ISOMORPHISMS FOR λ-RINGS (1971) (19)
Lecture 1: Transversally elliptic operators (1974) (19)
Fields Medallists' Lectures (1997) (17)
Pulling the strings (2005) (17)
A geometric construction of the discrete series for semisimple Lie groups (1977) (17)
MAGNETIC MONOPOLES AND THE YANG-BAXTER EQUATIONS (1991) (15)
The Jones-Witten invariants of knots (1990) (14)
Paul Dirac: The Dirac equation and geometry (1998) (13)
Green's functions for selfdual four manifolds (1981) (12)
Time evolution in a geometric model of a particle (2014) (12)
Errata to the Paper: On the Heat Equation and the Index Theorem. (1975) (12)
DUALITY IN MATHEMATICS AND PHYSICS (2008) (12)
Algebraic topology and elliptic operators (2010) (11)
Complex geometry of nuclei and atoms (2018) (11)
How research is carried out (1974) (11)
Paul Dirac: The Man and his Work (1998) (11)
Yang-Mills and bundles over algebraic curves (1981) (11)
A Shifted View of Fundamental Physics (2010) (11)
Geometric Models of Helium (2017) (10)
Anomalies and index theory (1984) (10)
Quantum physics and the topology of knots (1995) (10)
An interview with Michael Atiyah (1984) (10)
Maslov optimization theory: topological aspect (1998) (9)
The Encoding of Temporally Irregular and Regular Visual Patterns in the Human Brain (2008) (9)
Vector fields on manifolds. (2013) (8)
The Non-Existent Complex 6-Sphere (2016) (8)
A survey of K-theory (1977) (8)
Surveys in Differential Geometry VIII, Papers in Honor of Calabi, Lawson, Siu and Uhlenbeck (2003) (7)
Signature defects of cusps and values of L-functions (1983) (7)
Anyons in geometric models of matter (2016) (7)
Quantum field theory and low dimensional geometry (1990) (7)
Invariant differential operators and eigenspace representations (1980) (7)
The Role of Algebraic Topology in Mathematics (1966) (6)
THE FINE STRUCTURE CONSTANT (2018) (6)
The Harish-Chandra character (1980) (6)
Monopoles and Yang-Baxter equations (1995) (6)
Mathematics in the twentieth century (2000) (6)
THE WORK OF SIMON DONALDSON (1997) (6)
On the Work of Edward Witten (1990) (6)
The impact of Thom’s cobordism theory (2004) (6)
Abstracts of additional presentations made at the Royal Society Discussion Meeting ‘The nature of mathematical proof’ (2005) (5)
John Arthur Todd (1998) (5)
Equivariant Cohomology and Representations of the Symmetric Group (2000) (5)
Differential analysis : papers presented at the Bombay Colloquium, 1964 (1964) (4)
The Social Responsibility of Scientists (1999) (4)
Einstein and Geometry (2007) (4)
Michael Atiyah collected works (2004) (4)
The Influence of Computers and Informatics on Mathematics and its Teaching: Mathematics and the Computer Revolution (1986) (4)
Commentary on the article of manin (1985) (4)
Geometry and Physics (1996) (4)
Mathematics: Art and science (2005) (4)
Classical Groups and Classical Differential Operators on Manifolds (2010) (3)
The Relativistic Geometry and Dynamics of Electrons (2018) (3)
What Is Geometry? The 1982 Presidential Address (1982) (3)
APPENDIX I. THE INDEX THEOREM FOR MANIFOLDS WITH BOUNDARY (1965) (3)
A Nuclear-Weapon-Free World: Steps Along the Way (2000) (3)
Science for evil: the scientist's dilemma (1999) (3)
William Vallance Douglas Hodge (1977) (3)
М. Вернь Formal equivariant Â class, splines and multiplicities of the index of transversally elliptic operators (2018) (3)
The geometry and physics of knots: History and background (1990) (3)
Edinburgh Lectures on Geometry, Analysis and Physics (2010) (3)
Reflections on geometry and physics (1993) (3)
Hyperbolic differential equations and algebraic geometry (1968) (2)
Paul Dirac: Paul Dirac: aspects of his life and work (1998) (2)
THE GROTHENDIECK RING IN GEOMETRY AND TOPOLOGY (2010) (2)
Address of the President, Sir Michael Atiyah, O. M., given at the Anniversary Meeting on 30 November 1994 (1995) (2)
Benjamin Franklin and the Edinburgh Enlightenment1 (2006) (2)
A note on the tangents of a twisted cubic (1952) (2)
A Community of Scholars: Impressions of the Institute for Advanced Study (2011) (2)
The Interaction between Geometry and Physics (2006) (2)
Understanding the 6-Dimensional Sphere (2018) (2)
The millennium prize promblems : Clay Mathematics Institute Millennium Meeting, Collège de France, Paris, May 24-25, 2000 (2002) (2)
Bakerian Lecture, 1975: Global Geometry (2004) (2)
Introduction To Commutative Algebra, Student Economy Edition (2015) (2)
COMPLEX ANALYTIC CONNECTIONS IN FIBRE (2010) (2)
Representation theory of Lie groups : proceedings of the SRC/LMS Research Symposium on Representations of Lie Groups, Oxford, 28 June-15 July 1977 (1979) (2)
Geometry of Low-dimensional Manifolds: Representations of braid groups (1991) (1)
Riemann's Influence in Geometry, Analysis and Number Theory (2007) (1)
Eighty Years On (2011) (1)
Erratum to the Paper: A Geometric Construction of the Discrete Series for Semisimple Lie Groups (1980) (1)
Remarks on Morse Theory (1980) (1)
The challenge of computer mathematics. Discussion (2005) (1)
Note on Involutions (1977) (1)
Anniversary Address by the President of the Royal Society: Sir Michael Atiyah (1996) (1)
ISLAMIC PATTERNS AND THEIR SYMMETRIES (1994) (1)
Computing and the cultures of proving. Dicussion (2005) (1)
Raoul Harry Bott, FRS, 1923–2005 (2010) (1)
Vector Bundles on Algebraic Varieties: Papers presented at the Bombay Colloquium 1984 (1987) (1)
Address of the President, Sir Michael Atiyah, given at the Anniversary meeting on 29 November 1991 (1992) (1)
The European Mathematical Society (1991) (1)
Mathematics and the computer revolution (2016) (1)
Integral geometry and representation theory (1980) (1)
The Israeli-Palestinian Science Organization (2007) (1)
100 Years of Mathematics. (2000) (1)
Geometry and Physics: Where Are We Going? (2021) (1)
The Hirzebruch Signature Theorem for Conical Metrics (2016) (1)
Congurations of points (2010) (1)
THE WORK OF SERGE NOVIKOV (1997) (1)
Real and Complex Geometry in Four Dimensions (1980) (1)
William Vallance Douglas Hodge, 17 June 1903 - 7 July 1975 (1976) (1)
The geometry and physics of knots: The infinite-dimensional case (1990) (1)
GEOMETRY AND ANALYSIS Papers dedicated to the memory of V. K. Patodi (1984) (1)
Scalar curvature, flat Borromean rings, and the 3-body problem (2017) (1)
K-theory : lectures by M. F. Atiyah; Notes by D. W. Anderson (1967) (1)
Raoul Harry Bott. 24 September 1923 — 20 December 2005 (2007) (1)
Discrete Valuation Rings and Dedekind Domains (2018) (0)
The Feynman integral formulation (1990) (0)
Lacunas of hyperbolic differential equationes(講演記録) (1970) (0)
Lecture 9: The cohomology formula (1974) (0)
Anyon Networks from Geometric Models of Matter (2021) (0)
Geometry and analysis of Shimizu L-functions. (1982) (0)
CHAPTER 10. Some Inequalities (1988) (0)
LECTURES ON DIFFERENTIAL GEOMETRY (1966) (0)
Construction of Instantons (1994) (0)
MILLENNIUM LECTURE - CAIRO, 15 JANUARY 2000 (2001) (0)
Lecture 10: Applications (1974) (0)
Non-abelian moduli spaces (1990) (0)
Physics and mathematics of strings: Proceedings of a Royal Society Discussion Meeting, held on 8 and 9 December 1988 (1989) (0)
ARITHMETIC PHYSICS – ABEL LECTURE (2019) (0)
The geometry and physics of knots: Final comments (1990) (0)
New Developments in the Theory of Knots; The Geometry and Physics of Knots; The Geometry of Four‐Manifolds (1992) (0)
VI.90 William Vallance Douglas Hodge (2010) (0)
Lecture 5: The index homomorphism for G = S1 (1974) (0)
CHAPTER 12. Detailed Properties of the Metric (1988) (0)
TWISTED K-THEORY OLD AND NEW 3 General plan of the paper (2007) (0)
Paul Dirac: The monopole (1998) (0)
Lecture 6: The operators \bar \partial ^ \pm for G = S1 (1974) (0)
Józef Rotblat: My Friend (2007) (0)
CHAPTER 7. The 2-monopole Space (1988) (0)
Surveys in Differential Geometry XV A Shifted View of Fundamental Physics (2011) (0)
Математика и компьютерная революция@@@Mathematics and the computer revolution (2016) (0)
A UK Academy of Medicine? (1996) (0)
if-THEORY AND THE HOPF INVARIANT (2005) (0)
K-Theory and the Jones Polynomial (2018) (0)
CHAPTER 5. The Twistor Description (1988) (0)
Lecture 2: The index of transversally elliptic operators (1974) (0)
POWER OPERATIONS IN Z-THEORY (2005) (0)
Rings and Modules of Fraction (2018) (0)
Biodiversity A Joint Statement (1992) (0)
Quantum Field Theory and Low-Dimensional Geometry (Common Trends in Mathematics and Quantum Field Theories) (1991) (0)
Some applications of topological methods in algebraic geometry (1955) (0)
The mysteries of space (1992) (0)
A problem in Euclidean Geometry (2013) (0)
3 1 O ct 2 00 5 Twisted K-theory and cohomology (2005) (0)
CHAPTER 1. The Monopole Equations (1988) (0)
Address of the President, Sir Michael Atiyah, O. M., given at the Anniversary Meeting on 30 November 1993 (1994) (0)
The Heidelberg Laureate Forum on the moving frontier between mathematics and computer science (2017) (0)
CHAPTER 16. Background Material (1988) (0)
IN PRAISE OF PATTERN, SYMMETRY, UNITY & ISLAMIC ART (1994) (0)
A Geometer Explores the Universe (2012) (0)
Algebraic Topology – A Student's Guide: Characters and cohomology of finite groups (1972) (0)
The Impact of Physics on Geometry (1988) (0)
Address of the President, Sir Michael Atiyah, O. M., given at the Anniversary Meeting on 30 November 1992 (1993) (0)
Book Review: Lectures on mechanics (1994) (0)
CHAPTER 11. The Metric on M02 (1988) (0)
Lessons from the Scottish Enlightenment (2011) (0)
Viii. Final Perspectives Viii.6 Advice to a Young Mathematician (2008) (0)
THE GATEWAY FROM ISLAMIC PATTERNS TO INVARIANCE AND GROUPS (1994) (0)
The Riemann Hypothesis (2018) (0)
M. Hervé, Several Complex Variables: Local Theory (Oxford University Press, 1963), 26s. 6d. (1964) (0)
CHAPTER 8. Spectral Radii and the Conformal Structure (1988) (0)
Dirac operators coupled to vector potentials: (elliptic operators/index theory/characteristic classes/anomalies/gauge fields) (1989) (0)
CONFORMAL COMPACTIFICATIONS AND THEIR TOPOLOGY Objekttyp (2019) (0)
Working with Raoul Bott: From geometry to physics (2010) (0)
Geometry Topology and Physics (1988) (0)
CHAPTER 13. Geodesics on M02 (1988) (0)
The geometry and physics of knots , by Michael Atiyah. Pp 78. £6·95 (paperback), £20 (hardback). 1990. ISBN 0-521-39554-2, -39521-6 (Cambridge University Press) (1991) (0)
J ul 2 00 4 Twisted K-theory (0)
Lecture 4: The naturality of the index and the localization theorem (1974) (0)
Professor S.-T. Yau at 70 (2019) (0)
Paul Dirac: Antimatter (1998) (0)
CHAPTER 4. Hyperkahler Property of the Metric (1988) (0)
Jo Rotblat: Man With a Cause (2007) (0)
CHAPTER 6. Particles and Symmetric Products (1988) (0)
The Royal Society of Edinburgh Two-day Conference organised (2015) (0)
Todd function as weak analytic function (2019) (0)
Lecture 3: The excision and multiplicative properties (1974) (0)
CHAPTER 14. Particle Scattering (1988) (0)
O ct 2 00 2 Lagrangian surfaces with circular ellipse of curvature in complex space forms (2008) (0)
Thoughts of a Mathematician (2008) (0)
CHAPTER 15. Comparisons with KdV Solitons (1988) (0)
SCIENCE AND THE MILITARY : Warfare (2003) (0)
Collected papers of V. K. Patodi (1996) (0)
Lecture 7: Toral actions with finite isotropy groups (1974) (0)
THE MATHEMATICAL HERITAGE OF HENRI POINCARÉ (Proceedings of Symposia in Pure Mathematics, 39) (1985) (0)
CHAPTER 9. The Anti-self-dual Einstein Equations (1988) (0)
A Community of Scholars (2017) (0)
CHAPTER 3. Metric of Monopole Spaces (1988) (0)
William Leonard Edge (2018) (0)
CLASSIFICATION,IDENTIFICATION AND CONSTRUCTION OF THE SEVENTEEN TYPES OF TWO-DIMENSIONAL PERIODIC PATTERNS (1994) (0)
Invitation to Physicists (1991) (0)
ISLAMIC PATTERNSAND THEIR GEOMETRICAL STRUCTURES (1994) (0)
The Logarithm of the Dedekind q-Function (2004) (0)
What is a proof? Discussion (2005) (0)
John Arthur Todd, 23 August 1908 - 22 December 1994 (1996) (0)
msp MATHEMATICS AND CULTURE : GEOMETRY IN OXFORD 1960 – 1990 (2012) (0)
Early papers : general papers (1988) (0)
Rings and Ideals (2018) (0)
Mathematics and the real world (1998) (0)
2006 Fields Medals Awarded, Volume 53, Number 9 (2006) (0)
New developments in the theory and application of solitons : proceedings of a Royal Society Discussion Meeting held on 1 and 2 November, 1984 (1985) (0)
CHAPTER 2. Geometry of the Monopole Spaces (1988) (0)
Woods Hole (Commentary on [124]) (2017) (0)
MANIFOLDS OF PIECEWISE LINEAR MAPS AND A RELATED NORMED LINEAR SPACE (2007) (0)

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