Michael Atiyah | Academic Influence

Why Is Michael Atiyah Influential?

According to Wikipedia, Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry.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

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

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