Professor Tom Bridgeland FRS
School of Mathematics and Statistics
Royal Society Research Professor
+44 114 222 3747
Full contact details
School of Mathematics and Statistics
J18B
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
 Profile

After completing my undergraduate degree at Cambridge in 1995, I moved to Edinburgh to study for a PhD under Antony Maciocia. My thesis 'FourierMukai 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

I am an algebraic geometer with a particular interest in homological methods and interactions with string theory. My main focus is on properties of derived categories of coherent sheaves on algebraic varieties. These arise in string theory as categories of Dbranes, and are related via Kontsevich's famous homological mirror symmetry conjecture to Fukaya categories of symplectic manifolds.
Categories with similar properties and a more explicit flavour can be defined using representations of quivers. Other closely related mathematical areas I have an interest in are DonaldsonThomas invariants and Hall algebras.
 Publications

Show: Featured publications All publications
Featured publications
Journal articles
 Riemann–Hilbert problems for the resolved conifold and nonperturbative partition functions. Journal of Differential Geometry, 115(3), 395435. View this article in WRRO
 Riemann–Hilbert problems from Donaldson–Thomas theory. Inventiones mathematicae, 216(1), 69124. View this article in WRRO
 Scattering diagrams, Hall algebras and stability conditions. Algebraic Geometry, 4(5), 523561. View this article in WRRO
 Derived automorphism groups of K3 surfaces of Picard rank 1. Duke Mathematical Journal, 166(1), 75124. View this article in WRRO
 Quadratic differentials as stability conditions. Publications mathématiques de l'IHÉS, 121(1), 155278. View this article in WRRO
All publications
Journal articles
 Complex hyperkähler structures defined by Donaldson–Thomas invariants. Letters in Mathematical Physics, 111. View this article in WRRO
 Riemann–Hilbert problems for the resolved conifold and nonperturbative partition functions. Journal of Differential Geometry, 115(3), 395435. View this article in WRRO
 The monodromy of meromorphic projective structures. Transactions of the American Mathematical Society, 373, 63216367. View this article in WRRO
 Stability conditions and the A2 quiver. Advances in Mathematics, 365. View this article in WRRO
 RIEMANNHILBERT PROBLEMS FOR THE RESOLVED CONIFOLD. JOURNAL OF DIFFERENTIAL GEOMETRY, 115(3), 395435.
 Riemann–Hilbert problems from Donaldson–Thomas theory. Inventiones mathematicae, 216(1), 69124. View this article in WRRO
 Fourier–Mukai transforms for quotient varieties. Journal of Geometry and Physics, 122, 119127. View this article in WRRO
 Scattering diagrams, Hall algebras and stability conditions. Algebraic Geometry, 4(5), 523561. View this article in WRRO
 Derived automorphism groups of K3 surfaces of Picard rank 1. Duke Mathematical Journal, 166(1), 75124. View this article in WRRO
 Quadratic differentials as stability conditions. Publications mathématiques de l'IHÉS, 121(1), 155278. View this article in WRRO
 Stokes factors and multilogarithms. Journal fur die Reine und Angewandte Mathematik(682), 89128.
 Quantum groups via Hall algebras of complexes. Annals of Mathematics, 177(2), 739759.
 An introduction to motivic Hall algebras. Advances in Mathematics, 229(1), 102138.
 Stability conditions and Stokes factors. Inventiones mathematicae, 187(1), 6198.
 Hall algebras and curvecounting invariants. Journal of the American Mathematical Society, 24(4), 969998.
 Helices on del Pezzo surfaces and tilting Calabi–Yau algebras. Advances in Mathematics, 224(4), 16721716.
 Stability conditions on $K3$ surfaces. Duke Mathematical Journal, 141(2), 241291.
 Stability conditions on triangulated categories. Annals of Mathematics, 166(2), 317345.
 Stability Conditions on a NonCompact CalabiYau Threefold. Communications in Mathematical Physics, 266(3), 715733.
 A criterion for regularity of local rings. Comptes Rendus Mathematique, 342(10), 723726.
 Tstructures on some local Calabi–Yau varieties. Journal of Algebra, 289(2), 453483.
 FourierMukai transforms for K3 and elliptic fibrations. Journal of Algebraic Geometry, 11(4), 629657.
 Flops and derived categories. Inventiones Mathematicae, 147(3), 613632.
 The McKay correspondence as an equivalence of derived categories. View this article in WRRO
 Complex surfaces with equivalent derived categories. Mathematische Zeitschrift, 236(4), 677697.
 Equivalences of Triangulated Categories and FourierMukai Transforms. Bulletin of the London Mathematical Society, 31(1), 2534.
 FourierMukai transforms for elliptic surfaces. Journal für die reine und angewandte Mathematik (Crelles Journal), 1998(498), 115133.
 Stability Conditions and Kleinian Singularities. International Mathematics Research Notices.
 Derived categories of coherent sheaves, 563582.
 View this article in WRRO On the monodromy of the deformed cubic oscillator.
 View this article in WRRO A quantized RiemannHilbert problem in DonaldsonThomas theory.
 View this article in WRRO Geometry from DonaldsonThomas invariants.
Chapters
 Hall algebras and DoanldsonThomas invariants (pp. 75100). American Mathematical Society
Conference proceedings papers
 Hall algebras and DonaldsonThomas invariants (pp 75100) View this article in WRRO
 Spaces of stability conditions (pp 121)
Preprints
 Joyce structures on spaces of quadratic differentials I, arXiv.
 Complex hyperkähler structures defined by DonaldsonThomas invariants, arXiv.
 On the monodromy of the deformed cubic oscillator, arXiv.
 Complex surfaces with equivalent derived categories, arXiv.
 A quantized RiemannHilbert problem in DonaldsonThomas theory, arXiv.
 The monodromy of meromorphic projective structures, arXiv.
 RiemannHilbert problems for the resolved conifold, arXiv.
 RiemannHilbert problems from DonaldsonThomas theory, arXiv.
 Hall algebras and DonaldsonThomas 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 curvecounting invariants, arXiv.
 An introduction to motivic Hall algebras, arXiv.
 Helices on del Pezzo surfaces and tilting CalabiYau 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 noncompact CalabiYau threefold, arXiv.
 Stability conditions and Kleinian singularities, arXiv.
 Tstructures on some local CalabiYau 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.
 FourierMukai transforms for K3 and elliptic fibrations, arXiv.
 FourierMukai transforms for quotient varieties, arXiv.
 Equivalences of triangulated categories and FourierMukai transforms, arXiv.
 FourierMukai transforms for elliptic surfaces, arXiv.
 Research group
 Grants

Current grants, as Principal Investigator
Stability conditions, DonaldsonThomas invariants and cluster varieties RS Stability conditions, DT invariants and cluster varieties EC Geometry from DonaldsonThomas invariants EPSRC
 Professional activities and memberships

Talks
 From DonaldsonThomas invariants to hyperkahler structures, Simons Centre meeting, January 2021.
 Geometry from DonaldsonThomas invariants, Shafarevich seminar, June 2020.
 Wallcrossing for DonaldsonThomas invariants (PDF, 276KB), Oxford, September 2017 (beamer slides).
 Stability conditions and quivers (PDF, 406KB), Stavanger, September 2015 (beamer slides).
 Stability conditions and wallcrossing: 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 wallcrossing, April 2012.
 A video of an introductory lecture on derived categories in algebraic geometry, March 2007.