Imperial College London

Professor Sir Simon Donaldson FRS

Faculty of Natural SciencesDepartment of Mathematics

Chair in Pure Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8559s.donaldson Website

 
 
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Location

 

674Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

82 results found

Donaldson S, 2021, ATIYAH'S WORK ON HOLOMORPHIC VECTOR BUNDLES AND GAUGE THEORIES, BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 58, Pages: 567-610, ISSN: 0273-0979

Journal article

Donaldson S, 2021, INTRODUCTION TO THE ATIYAH ISSUE, BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 58, Pages: 479-480, ISSN: 0273-0979

Journal article

Donaldson S, 2021, DEFORMATIONS OF MULTIVALUED HARMONIC FUNCTIONS, QUARTERLY JOURNAL OF MATHEMATICS, Vol: 72, Pages: 199-235, ISSN: 0033-5606

Journal article

Donaldson S, 2019, An elliptic boundary value problem for G2-structures, Annales de l'Institut Fourier, Vol: 68, Pages: 2783-2809, ISSN: 0373-0956

We show that the G2 holonomy equation on a manifold with boundary, with prescribed 3-form on the boundary, is elliptic. The main point is to set up a suitable linear elliptic boundary value problem. This result leads to a deformation theory. In particular we establish the existence of certain G2 cobordisms between two small deformations of a Calabi-Yau 3-fold.

Journal article

Donaldson SK, 2018, Remarks on G2 structures with boundary, Journal of Differential Geometry Conference

Conference paper

Donaldson SK, 2018, Stability of algebraic varieties and Kahler geometry, American-Mathematical-Society Summer Research Institute on Algebraic Geometry, Publisher: AMER MATHEMATICAL SOC, Pages: 199-221, ISSN: 2324-707X

Conference paper

Donaldson S, Sun S, 2017, Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, II, Journal of Differential Geometry, Vol: 107, Pages: 327-371, ISSN: 0022-040X

We study Gromov–Hausdorff limits of Kähler–Einstein manifolds, in particular, their singularities, and connections with algebraic geometry. This is a continuation of our previous work.

Journal article

Donaldson S, 2016, Kahler-Einstein metrics and algebraic structures on limit spaces, Conference on Geometry and Topology, Publisher: INTERNATIONAL PRESS INC BOSTON, Pages: 85-94, ISSN: 1052-9233

Conference paper

Chen X, Donaldson S, Sun S, 2015, Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2 pi, Journal of the American Mathematical Society, Vol: 28, Pages: 199-234, ISSN: 0894-0347

This is the second of a series of three papers which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle is less than 2$ {\pi }$. We show that these are in a natrual way projective algebraic varieties. In the case when the limiting variety and the limiting divisor are smooth we show that the limiting metric also has standard cone singularities.

Journal article

Chen X, Donaldson S, Sun S, 2015, KAHLER-EINSTEIN METRICS ON FANO MANIFOLDS. I: APPROXIMATION OF METRICS WITH CONE SINGULARITIES, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 28, Pages: 183-197, ISSN: 0894-0347

Journal article

Chen X, Donaldson S, Sun S, 2015, Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2 pi and completion of the main proof, Journal of the American Mathematical Society, Vol: 28, Pages: 235-278, ISSN: 0894-0347

This is the third and final article in a series which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2$ \pi $. We also put all our technical results together to complete the proof of the main theorem.

Journal article

Donaldson S, Sun S, 2014, Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, ACTA MATHEMATICA, Vol: 213, Pages: 63-106, ISSN: 0001-5962

Journal article

Chen X-X, Donaldson SK, 2014, Integral bounds on curvature and Gromov-Hausdorff limits, JOURNAL OF TOPOLOGY, Vol: 7, Pages: 543-556, ISSN: 1753-8416

Journal article

Donaldson SK, 2014, b-STABILITY AND BLOW-UPS, PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, Vol: 57, Pages: 125-137, ISSN: 0013-0915

Journal article

Chen X, Donaldson S, Sun S, 2014, Kahler-Einstein Metrics and Stability, INTERNATIONAL MATHEMATICS RESEARCH NOTICES, Vol: 2014, Pages: 2119-2125, ISSN: 1073-7928

Journal article

Chen X-X, Donaldson SK, 2013, VOLUME ESTIMATES FOR KAHLER-EINSTEIN METRICS: THE THREE-DIMENSIONAL CASE, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 93, Pages: 175-189, ISSN: 0022-040X

Journal article

Chen X-X, Donaldson SK, 2013, VOLUME ESTIMATES FOR KAHLER-EINSTEIN METRICS AND RIGIDITY OF COMPLEX STRUCTURES, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 93, Pages: 191-201, ISSN: 0022-040X

Journal article

Donaldson S, 2012, Kahler metrics with cone singularities along a divisor, Essays in mathematics and its applications : In honor of Stephen Smale's 80th birthday., Editors: Pardalos, Rassias, Publisher: Springer, Pages: 49-79, ISBN: 978-3-642-28820-3

We develop some foundations for the study of Kahler-Einstein metrics withcone singularities transverse to a divisor. The main goal is a treatment of thedeformation of the cone angle.

Book chapter

Donaldson SK, 2009, Constant Scalar Curvature Metrics on Toric Surfaces, GEOMETRIC AND FUNCTIONAL ANALYSIS, Vol: 19, Pages: 83-136, ISSN: 1016-443X

Journal article

Donaldson SK, 2009, Some numerical results in complex differential geometry, Pure and Applied Mathematics Quarterly, Vol: 5, Pages: 571-618, ISSN: 1558-8599

Journal article

Donaldson SK, 2008, Some problems in differential geometry and topology, NONLINEARITY, Vol: 21, Pages: T157-T164, ISSN: 0951-7715

Journal article

Donaldson SK, 2008, Extremal metrics on toric surfaces: A continuity method, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 79, Pages: 389-432, ISSN: 0022-040X

Journal article

Donaldson SK, 2008, A generalised Joyce construction for a family of nonlinear partial differential equations

We explain a simple construction of solutions to a family of PDE's in twodimensions which includes that defining zero scalar curvature Kahler metrics,with two Killing fields, and the affine maximal equation.

Working paper

Donaldson S, Fine J, 2006, Tonic anti-self-dual 4-manifolds via complex geometry, MATHEMATISCHE ANNALEN, Vol: 336, Pages: 281-309, ISSN: 0025-5831

Journal article

Donaldson SK, 2005, Lower bounds on the Calabi functional, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 70, Pages: 453-472, ISSN: 0022-040X

Journal article

Auroux D, Donaldson SK, Katzarkov L, 2005, Singular Lefschetz pencils, GEOMETRY & TOPOLOGY, Vol: 9, Pages: 1043-1114, ISSN: 1465-3060

Journal article

Donaldson SK, 2005, Interior estimates for solutions of Abreu's equation, COLLECTANEA MATHEMATICA, Vol: 56, Pages: 103-142, ISSN: 0010-0757

Journal article

Donaldson SK, 2005, Scalar curvature and projective embeddings, II, Quarterly Journal of Mathematics, Vol: 56, Pages: 345-356, ISSN: 0033-5606

Journal article

Auroux D, Donaldson SK, Katzarkov L, Yotov Met al., 2004, Fundamental groups of complements of plane curves and symplectic invariants, TOPOLOGY, Vol: 43, Pages: 1285-1318, ISSN: 0040-9383

Journal article

Donaldson S, Smith I, 2003, Lefschetz pencils and the canonical class for symplectic four-manifolds, TOPOLOGY, Vol: 42, Pages: 743-785, ISSN: 0040-9383

Journal article

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