Professor Tom Bridgeland FRS
School of Mathematical and Physical Sciences
Royal Society Research Professor
t.bridgeland@sheffield.ac.uk
J18B, Hicks Building
Full contact details
Professor Tom Bridgeland FRS
School of Mathematical and Physical Sciences
J18B
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
School of Mathematical and Physical Sciences
J18B
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Profile
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After completing my undergraduate degree at Cambridge in 1995, I moved to Edinburgh to study for a PhD under Antony Maciocia. My thesis 'Fourier-Mukai transforms for surfaces and moduli spaces of stable sheaves' was completed in 1998.
I held a series of postdoctoral positions at Edinburgh and the University of Sheffield, including a Royal Society University Research Fellowship.
In 2012 I was elected to a Senior Research Fellowship at All Souls College, Oxford. I resigned this in 2013 to return to a position at Sheffield.
- Research interests
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I am interested in algebraic and enumerative geometry and links with mathematical physics. In the first part of my career I did a lot of work with derived and triangulated categories. In particular, I introduced the space of stability conditions on a triangulated category and studied it in examples. Later I did some work on generalised Donaldson-Thomas invariants. More recently I have been trying to use these invariants to define geometric structures on spaces of stability conditions. All these topics are purely mathematical in nature, but are heavily motivated by ideas from topological string theory.
- Publications
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Show: Featured publications All publications
Featured publications
Journal articles
- Riemann–Hilbert problems for the resolved conifold and non-perturbative partition functions. Journal of Differential Geometry, 115(3), 395-435.
- Riemann-Hilbert problems from Donaldson-Thomas theory. Inventiones Mathematicae, 216(1), 69-124. View this article in WRRO
- Scattering diagrams, Hall algebras and stability conditions. Algebraic Geometry, 4(5), 523-561. View this article in WRRO
- Derived automorphism groups of K3 surfaces of Picard rank 1. Duke Mathematical Journal, 166(1), 75-124. View this article in WRRO
- Quadratic differentials as stability conditions. Publications mathématiques de l'IHÉS. View this article in WRRO
All publications
Journal articles
- Joyce structures on spaces of quadratic differentials. Geometry & Topology, 29(5), 2695-2731. View this article in WRRO
- Resurgence and Riemann–Hilbert problems for elliptic Calabi–Yau threefolds. Communications in Mathematical Physics, 406(6). View this article in WRRO
- Joyce structures and their twistor spaces. Advances in Mathematics, 462. View this article in WRRO
- Tau functions from Joyce structures. Symmetry, Integrability and Geometry: Methods and Applications, 20(112). View this article in WRRO
- On the monodromy of the deformed cubic oscillator. Mathematische Annalen, 385(1-2), 193-258. View this article in WRRO
- Complex hyperkähler structures defined by Donaldson–Thomas invariants. Letters in Mathematical Physics, 111.
- Riemann–Hilbert problems for the resolved conifold and non-perturbative partition functions. Journal of Differential Geometry, 115(3), 395-435.
- The monodromy of meromorphic projective structures. Transactions of the American Mathematical Society, 373, 6321-6367. View this article in WRRO
- Stability conditions and the A2 quiver. Advances in Mathematics, 365. View this article in WRRO
- Riemann-Hilbert problems from Donaldson-Thomas theory. Inventiones Mathematicae, 216(1), 69-124. View this article in WRRO
- Fourier–Mukai transforms for quotient varieties. Journal of Geometry and Physics, 122, 119-127. View this article in WRRO
- Scattering diagrams, Hall algebras and stability conditions. Algebraic Geometry, 4(5), 523-561. View this article in WRRO
- Derived automorphism groups of K3 surfaces of Picard rank 1. Duke Mathematical Journal, 166(1), 75-124. View this article in WRRO
- Quadratic differentials as stability conditions. Publications mathématiques de l'IHÉS. View this article in WRRO
- Quantum groups via Hall algebras of complexes. Annals of Mathematics, 177(2), 739-759.
- Stokes factors and multilogarithms. crll, 2013(682), 89-128.
- An introduction to motivic Hall algebras. Advances in Mathematics, 229(1), 102-138.
- Stability conditions and Stokes factors. Inventiones mathematicae, 187(1), 61-98.
- Helices on del Pezzo surfaces and tilting Calabi–Yau algebras. Advances in Mathematics, 224(4), 1672-1716.
- Stability conditions on K3 surfaces. Duke Mathematical Journal, 141(2).
- Stability conditions on triangulated categories. Annals of Mathematics, 166(2), 317-345.
- Derived categories of coherent sheaves, 563-582.
- Stability Conditions on a Non-Compact Calabi-Yau Threefold. Communications in Mathematical Physics, 266(3), 715-733.
- T-structures on some local Calabi–Yau varieties. Journal of Algebra, 289(2), 453-483.
- Fourier-Mukai transforms for K3 and elliptic fibrations. Journal of Algebraic Geometry, 11(4), 629-657.
- Flops and derived categories. Inventiones Mathematicae, 147(3), 613-632.
- Complex surfaces with equivalent derived categories. Mathematische Zeitschrift, 236(4), 677-697.
- The McKay correspondence as an equivalence of derived categories. J. Amer. Math. Soc., 14, 535-554.
- Equivalences of Triangulated Categories and Fourier-Mukai Transforms. Bulletin of the London Mathematical Society, 31(1), 25-34.
- Fourier-Mukai transforms for elliptic surfaces. Journal für die reine und angewandte Mathematik (Crelles Journal), 1998(498), 115-133.
- Scattering diagrams, Hall algebras and stability conditions. Algebraic Geometry, 523-561.
- Hall algebras and curve-counting invariants. Journal of the American Mathematical Society, 24(4), 969-998.
- Stability Conditions and Kleinian Singularities. International Mathematics Research Notices.
- A criterion for regularity of local rings. Comptes Rendus. Mathématique, 342(10), 723-726.
Book chapters
- Geometry from Donaldson-Thomas invariants In Novikov S, Krichever I, Ogievetsky O & Shlosman S (Ed.), Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry (pp. 1-66). American Mathematical Society View this article in WRRO
- Hall algebras and Doanldson-Thomas
invariants (pp. 75-100). American Mathematical
Society
Conference proceedings
- Spaces of stability conditions (pp 1-21)
Preprints
- A quantized Riemann-Hilbert problem in Donaldson-Thomas theory, arXiv.
- Joyce structures and poles of Painlevé equations, arXiv.
- Clusters, twistors and stability conditions I, arXiv.
- On the monodromy of the deformed cubic oscillator, arXiv.
- Complex surfaces with equivalent derived categories, arXiv.
- The monodromy of meromorphic projective structures, arXiv.
- Riemann-Hilbert problems for the resolved conifold, arXiv.
- Riemann-Hilbert problems from Donaldson-Thomas theory, arXiv.
- Hall algebras and Donaldson-Thomas invariants, arXiv.
- Scattering diagrams, Hall algebras and stability conditions, arXiv.
- Stability conditions and the $A_2$ quiver, arXiv.
- Derived automorphism groups of K3 surfaces of Picard rank 1, arXiv.
- Quadratic differentials as stability conditions, arXiv.
- Quantum groups via Hall algebras of complexes, arXiv.
- Stokes factors and multilogarithms, arXiv.
- Hall algebras and curve-counting invariants, arXiv.
- An introduction to motivic Hall algebras, arXiv.
- Helices on del Pezzo surfaces and tilting Calabi-Yau algebras, arXiv.
- Stability conditions and Stokes factors, arXiv.
- Spaces of stability conditions, arXiv.
- A criterion for regularity of local rings, arXiv.
- Derived categories of coherent sheaves, arXiv.
- Stability conditions on a non-compact Calabi-Yau threefold, arXiv.
- Stability conditions and Kleinian singularities, arXiv.
- T-structures on some local Calabi-Yau varieties, arXiv.
- Stability conditions on K3 surfaces, arXiv.
- Stability conditions on triangulated categories, arXiv.
- Flops and derived categories, arXiv.
- Mukai implies McKay: the McKay correspondence as an equivalence of derived categories, arXiv.
- Fourier-Mukai transforms for K3 and elliptic fibrations, arXiv.
- Fourier-Mukai transforms for quotient varieties, arXiv.
- Equivalences of triangulated categories and Fourier-Mukai transforms, arXiv.
- Fourier-Mukai transforms for elliptic surfaces, arXiv.
- Riemann–Hilbert problems for the resolved conifold and non-perturbative partition functions. Journal of Differential Geometry, 115(3), 395-435.
- Research group
- Grants
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Current grants, as Principal Investigator
Stability conditions, Donaldson-Thomas invariants and cluster varieties RS Stability conditions, DT invariants and cluster varieties EC Geometry from Donaldson-Thomas invariants EPSRC
- Professional activities and memberships
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Talks
- From Donaldson-Thomas invariants to hyperkahler structures, Simons Centre meeting, January 2021.
- Geometry from Donaldson-Thomas invariants, Shafarevich seminar, June 2020.
- Wall-crossing for Donaldson-Thomas invariants (PDF, 276KB), Oxford, September 2017 (beamer slides).
- Stability conditions and quivers (PDF, 406KB), Stavanger, September 2015 (beamer slides).
- Stability conditions and wall-crossing: Three talks at the AMS algebraic geometry festival in July 2015.
- Lecture notes for an introductory course on derived categories of coherent sheaves (PDF, 369KB), Warwick, September 2014.
- If you want to learn about stability conditions, watch Daniel Huybrechts' talks at the Issac Newton Institute.
- Three talks on stability conditions from 2013: the first two are introductory, the last is about a class of examples relating to moduli spaces of quadratic differentials.
- Four lectures on stability and wall-crossing, April 2012.
- A video of an introductory lecture on derived categories in algebraic geometry, March 2007.