#422

Most Influential Person

English mathematician and Fields medalist

Simon Donaldsonmathematics Degrees

Mathematics

#18

World Rank

#68

Historical Rank

Differential Topology

#4

World Rank

#4

Historical Rank

Differential Geometry

#3

World Rank

#6

Historical Rank

Geometry

#5

World Rank

#12

Historical Rank

Mathematics

- PhD Mathematics University of Oxford

According to Wikipedia, Sir Simon Kirwan Donaldson is an English mathematician known for his work on the topology of smooth four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.

- Geometry of four-manifolds (1990) (1691)
- Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles (1985) (1118)
- An application of gauge theory to four-dimensional topology (1983) (825)
- Scalar Curvature and Stability of Toric Varieties (2002) (815)
- Scalar Curvature and Projective Embeddings, I (2001) (638)
- Polynomial invariants for smooth four-manifolds (1990) (592)
- Twisted harmonic maps and the self-duality equations (1987) (457)
- Infinite determinants, stable bundles and curvature (1987) (425)
- A new proof of a theorem of Narasimhan and Seshadri (1983) (383)
- The orientation of Yang-Mills moduli spaces and 4-manifold topology (1987) (376)
- Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities (2012) (370)
- Symplectic submanifolds and almost-complex geometry (1996) (368)
- Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2\pi\ and completion of the main proof (2013) (320)
- Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2 (2012) (310)
- Nahm's equations and the classification of monopoles (1984) (302)
- Gauge Theory in higher dimensions, II (2009) (277)
- Floer Homology Groups in Yang-Mills Theory (2002) (271)
- Lefschetz pencils on symplectic manifolds (1999) (270)
- Lower bounds on the Calabi functional (2005) (258)
- 4-MANIFOLDS AND KIRBY CALCULUS (Graduate Studies in Mathematics 20) By R OBERT E. G OMPF and A NDRÁS I. S TIPSICZ : 558 pp., US$65.00, ISBN 0-8218-0994-6 (American Mathematical Society, Providence, RI, 1999). (2001) (253)
- Instantons and geometric invariant theory (1984) (250)
- Connections, cohomology and the intersection forms of 4-manifolds (1986) (243)
- Irrationality and the $h$-cobordism conjecture (1987) (237)
- The Seiberg-Witten equations and 4-manifold topology (1996) (234)
- Kähler Metrics with Cone Singularities Along a Divisor (2011) (233)
- Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry (2012) (216)
- Some numerical results in complex differential geometry (2005) (178)
- REMARKS ON GAUGE THEORY, COMPLEX GEOMETRY AND 4-MANIFOLD TOPOLOGY (1997) (178)
- Quasiconformal 4-manifolds (1989) (166)
- Constant Scalar Curvature Metrics on Toric Surfaces (2008) (161)
- Kahler geometry on toric manifolds, and some other manifolds with large symmetry (2008) (160)
- Connected sums of self-dual manifolds and deformations of singular spaces (1989) (142)
- Interior estimates for solutions of Abreu's equation (2004) (139)
- Scalar curvature and projective embeddings, II (2004) (138)
- Boundary value problems for Yang—Mills fields (1992) (136)
- Two-forms on four-manifolds and elliptic equations (2006) (125)
- Floer’s work on instanton homology, knots and surgery (1995) (122)
- Pin structures on low-dimensional manifolds (1991) (110)
- Extremal metrics on toric surfaces: a continuity method (2008) (108)
- Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves (2002) (108)
- Kahler-Einstein metrics and stability (2012) (104)
- Singular Lefschetz pencils (2004) (99)
- Holomorphic Discs and the Complex Mounge-Amperè equation (2001) (82)
- Lefschetz pencils and the canonical class for symplectic four-manifolds (2000) (76)
- Moment maps and diffeomorphisms (2002) (69)
- Stability, birational transformations and the Kahler-Einstein problem (2010) (60)
- Geometry of Low-dimensional Manifolds: Yang-Mills invariants of four-manifolds (1991) (54)
- Geometry of Low-Dimensional Manifolds (1991) (52)
- Self-dual connections and the topology of smooth 4-manifolds (1983) (52)
- Fundamental groups of complements of plane curves and symplectic invariants (2002) (51)
- Integral bounds on curvature and Gromov–Hausdorff limits (2011) (49)
- DIFFERENTIAL GEOMETRY OF COMPLEX VECTOR BUNDLES (1989) (49)
- Topological Field Theories and formulae of Casson and Meng{Taubes (1999) (46)
- Adiabatic Limits of Co-associative Kovalev–Lefschetz Fibrations (2016) (42)
- Nahm's equations and free-boundary problems (2007) (40)
- Fukaya-Floer homology and gluing formulae for polynomial invariants (1995) (34)
- Moment maps in differential geometry (2003) (34)
- Conjectures in Kahler geometry (2008) (33)
- The Ding Functional, Berndtsson Convexity and Moment Maps (2015) (31)
- Rational and ruled symplectic 4-manifolds (1991) (30)
- Discussion of the Kähler-Einstein problem (2009) (27)
- Gauge Theory and Four-Manifold Topology (1994) (25)
- TOPOLOGY AND ANALYSIS The Atiyah-Singer Index Formula and Gauge-Theoretic Physics (1986) (24)
- The approximation of instantons (1993) (22)
- Algebraic families of constant scalar curvature K\"ahler metrics (2015) (20)
- Numerical approximations to extremal metrics on toric surfaces (2008) (20)
- Calabi-Yau metrics on Kummer surfaces as a model glueing problem (2010) (18)
- On the topology of algebraic surfaces (1991) (17)
- Extremal metrics on toric surfaces, I (2006) (17)
- Symplectic Geometry: Complex cobordism, Ashtekar's equations and diffeomorphisms (1994) (15)
- Different faces of geometry (2004) (15)
- Compactification and completion of Yang-Mills moduli spaces (1989) (15)
- Stability of algebraic varieties and Kähler geometry (2017) (15)
- SOME RECENT DEVELOPMENTS IN KÄHLER GEOMETRY AND EXCEPTIONAL HOLONOMY (2018) (15)
- Conjectures in Kaehler geometry (2002) (14)
- Vector Bundles in Algebraic Geometry: Floer homology and algebraic geometry (1995) (14)
- COMPLEX DIFFERENTIAL GEOMETRY (AMS/IP Studies in Advanced Mathematics 18) By F ANGYANG Z HENG : 264 pp., US$49.00, ISBN 0-8218-2163-6 (American Mathematical Society/International Press, Providence, RI, 2000). (2002) (13)
- Some problems in differential geometry and topology (2008) (12)
- A note on the \alpha-invariant of the Mukai-Umemura 3-fold (2007) (10)
- Lectures on Lie groups and geometry (2008) (10)
- Volume estimates for K\"ahler-Einstein metrics and rigidity of complex structures (2011) (9)
- The Geometry of 4-Manifolds (2010) (9)
- The Geometry of 4-Manifolds (2010) (9)
- Lefschetz pencils and mapping class groups (2004) (9)
- Boundary value problems in dimensions seven, four and three related to exceptional holonomy (2017) (8)
- Flat algebraic manifolds (1991) (8)
- Deformations Of Multivalued Harmonic Functions (2019) (8)
- Complex curves and surgery (1988) (8)
- Lie Algebra Theory without Algebra (2007) (8)
- A generalised Joyce construction for a family of nonlinear partial differential equations (2008) (8)
- Gauge Theory: Mathematical Applications (2006) (7)
- Toric Anti-self-dual 4-manifolds Via Complex Geometry (2006) (7)
- Kahler-Einstein metrics and algebraic geometry (2017) (6)
- b-Stability and Blow-Ups (2011) (6)
- K\"ahler-Einstein metrics and algebraic structures on limit spaces (2016) (5)
- Remarks on $G_{2}$-manifolds with boundary (2018) (5)
- CHAPTER 14 – One Hundred Years of Manifold Topology (1999) (5)
- a Pseudoholomorphic Curve ? (2005) (4)
- Yang-Mills Theory and Geometry (2005) (4)
- On the Work of Louis Nirenberg (2011) (4)
- MATHEMATICAL USES OF GAUGE THEORY (2008) (4)
- Atiyah’s work on holomorphic vector bundles and gauge theories (2021) (3)
- Skyrme fields and instantons (1991) (3)
- Karen Uhlenbeck and the Calculus of Variations (2019) (3)
- Geometry of Low-Dimensional Manifolds : Symplectic Manifolds and Jones-Witten Theory (1991) (2)
- 4-Manifolds with indefinite intersection form (1985) (2)
- An elliptic boundary value problem for $G_{2}$ structures (2018) (2)
- An elliptic boundary value problem for G2-structures (2019) (2)
- The Yang-Mills equations on Kahler manifolds (1982) (2)
- THE FLOER MEMORIAL VOLUME (Progress in Mathematics 133) Edited by Helmut Hofer, Clifford H. Taubes, et al.: 685 pp., DM.138., ISBN 3 7643 5044 X (Birkhäuser, 1995) (1997) (2)
- HELICES AND VECTOR BUNDLES (Seminaire Rudakov) (1991) (2)
- Boundary Value Problems in Dimensions 7, 4 and 3 Related to Exceptional Holonomy (2018) (2)
- Geometry of Low-dimensional Manifolds: Representations of braid groups (1991) (1)
- Finite groups of hyperbolic isometries (1991) (1)
- Geometry of Low-dimensional Manifolds: Introduction (1991) (1)
- Floer homology groups in Yang–Mills theory: The Floer homology groups (2002) (1)
- Memories of Sir Michael Atiyah (2019) (1)
- A journey through the mathematical world of Karen Uhlenbeck (2022) (1)
- Geometry of low-dimensional manifolds 2, Sympletic manifolds and Jones-Witten theory / : proceedings of the Durham Symposium, July 1989. (1990) (1)
- Ordinary differential equations (2011) (0)
- Geometric And Functional Analysis CONSTANT SCALAR CURVATURE METRICS ON TORIC SURFACES (2009) (0)
- Topology and related topics (2017) (0)
- Elliptic functions and integrals (2011) (0)
- Geometry of Low-dimensional Manifolds: FLOER'S INSTANTON HOMOLOGY GROUPS (1991) (0)
- Applications of the Euler characteristic (2011) (0)
- Contrasts in Riemann surface theory (2011) (0)
- Floer homology groups in Yang–Mills theory: Floer homology and 4-manifold invariants (2002) (0)
- FOUR‐MANIFOLD THEORY (Contemporary Mathematics, 35). (1986) (0)
- Proof of the Main Theorem (2011) (0)
- The Work of Peter B. Kronheimer (1994) (0)
- Gauge theory and algebraic surfaces : proceedings of the Durham symposium, July 1989 (1990) (0)
- Calculus on surfaces (2011) (0)
- Fe b 20 09 Gauge theory in higher dimensions , II (2021) (0)
- New Developments in the Theory of Knots; The Geometry and Physics of Knots; The Geometry of Four‐Manifolds (1992) (0)
- SURVEYS IN DIFFERENTIAL GEOMETRY (Supplement to the Journal of Differential Geometry 1) (1995) (0)
- Maps between Riemann surfaces (2011) (0)
- Gauge theory and tubular ends (2002) (0)
- On some recent developments in Kähler geometry (2013) (0)
- The Uniformisation Theorem (2011) (0)
- Meromorphic functions and the Main Theorem for compact Riemann surfaces (2011) (0)
- Yau and differential geometry (2019) (0)
- Geometry of Low-dimensional Manifolds: SYMPLECTIC GEOMETRY (1991) (0)
- Floer homology groups in Yang–Mills theory: Introduction (2002) (0)
- Divisors, line bundles and Jacobians (2011) (0)
- MOMENT MAPS AND DIFFEOMORPHISMSt (2016) (0)
- Mathematical aspects of gauge theory : lecture notes (2017) (0)
- Geometry of Low-dimensional Manifolds: Acknowledgments (1991) (0)
- Names of Participants (1991) (0)
- Associative submanifolds and gradient cycles (2020) (0)
- IRRATIONALITY AND THE Λ-COBORDISM CONJECTURE (2008) (0)
- Closed 3-forms in five dimensions and embedding problems (2022) (0)
- Floer homology groups in Yang–Mills theory: Further directions (2002) (0)
- Mappings and moduli (2011) (0)
- Floer homology groups in Yang–Mills theory: Basic material (2002) (0)
- Gauge theory on Calabi-Yau manifolds (1997) (0)
- Symplectic manifolds and Jones-Witten theory : proceedings of the Durham symposium, July 1989 (1990) (0)
- The ADHM construction of Yang-Mills instantons (2022) (0)
- Moduli and deformations (2011) (0)
- Gauge Theory and Smooth Structures on 4-Manifolds (2020) (0)
- Book Review: Topology of gauge fields and condensed matter (1995) (0)
- Differential Geometric Methods in Low-dimensional Topology (2008) (0)
- Fredholm topology and enumerative geometry: reflections on some words of Michael Atiyah (2022) (0)
- Reducible connections and cup products (2002) (0)

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