Professor Tom Bridgeland FRS
School of Mathematical and Physical Sciences
Royal Society Research Professor
t.bridgeland@sheffield.ac.uk
+44 114 222 3747
+44 114 222 3747
J18B, Hicks Building
Full contact details
Professor Tom Bridgeland FRS
School of Mathematical and Physical Sciences
J18B
Hicks Building
Hounsfield Road
91Ö±²¥
S3 7RH
School of Mathematical and Physical Sciences
J18B
Hicks Building
Hounsfield Road
91Ö±²¥
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 91Ö±²¥, 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 91Ö±²¥.
- 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
- . Journal of Differential Geometry, 115(3), 395-435.
- . Inventiones mathematicae, 216(1), 69-124.
- . Algebraic Geometry, 4(5), 523-561.
- . Duke Mathematical Journal, 166(1), 75-124.
- . Publications mathématiques de l'IHÉS, 121(1), 155-278.
All publications
Journal articles
- . Letters in Mathematical Physics, 111.
- . Journal of Differential Geometry, 115(3), 395-435.
- . Transactions of the American Mathematical Society, 373, 6321-6367.
- . Advances in Mathematics, 365.
- . Inventiones mathematicae, 216(1), 69-124.
- . Journal of Geometry and Physics, 122, 119-127.
- . Algebraic Geometry, 4(5), 523-561.
- . Duke Mathematical Journal, 166(1), 75-124.
- . Publications mathématiques de l'IHÉS, 121(1), 155-278.
- . Journal fur die Reine und Angewandte Mathematik(682), 89-128.
- . Annals of Mathematics, 177(2), 739-759.
- . Advances in Mathematics, 229(1), 102-138.
- . Inventiones mathematicae, 187(1), 61-98.
- . Journal of the American Mathematical Society, 24(4), 969-998.
- . Advances in Mathematics, 224(4), 1672-1716.
- . Duke Mathematical Journal, 141(2), 241-291.
- Stability conditions on K3 surfaces. Duke Math. J., 141, 241-291.
- . Annals of Mathematics, 166(2), 317-345.
- Stability conditions on triangulated categories. Ann. Math. (2), 166, 317-345.
- Stability conditions on triangulated categories. Ann. Math. (2), 166, 317-345.
- . Communications in Mathematical Physics, 266(3), 715-733.
- . Comptes Rendus Mathematique, 342(10), 723-726.
- . Journal of Algebra, 289(2), 453-483.
- . Journal of Algebraic Geometry, 11(4), 629-657.
- Fourier-Mukai transforms for K3 and elliptic fibrations. J. Alg. Geom., 11, 629-657.
- Fourier-Mukai transforms for K3 and elliptic fibrations. J. Algebraic Geom., 11, 629-657.
- Flops and derived categories. Invent. Math., 147, 613-632.
- . Inventiones Mathematicae, 147(3), 613-632.
- .
- . Mathematische Zeitschrift, 236(4), 677-697.
- The McKay correspondence as an equivalence of derived categories. J. Amer. Math. Soc., 14, 535-554.
- Complex surfaces with equivalent derived categories. Math. Z., 236, 677-697.
- Complex surfaces with equivalent derived categories. Math. Z., 236, 677-697.
- . Bulletin of the London Mathematical Society, 31(1), 25-34.
- Fourier-Mukai transforms for elliptic surfaces. J. Reine Angew. Math., 498, 115-133.
- . Journal für die reine und angewandte Mathematik (Crelles Journal), 1998(498), 115-133.
- . International Mathematics Research Notices.
- , 563-582.
- On the monodromy of the deformed cubic oscillator.
- A quantized Riemann-Hilbert problem in Donaldson-Thomas theory.
- Geometry from Donaldson-Thomas invariants.
- . Stability conditions on triangulated categories.
- . Fourier-Mukai transforms for quotient varieties.
- . Stability conditions on K3 surfaces.
- . Stability conditions on K3 surfaces.
- . T-structures on some local Calabi-Yau varieties.
Chapters
- , Integrability, Quantization, and Geometry (pp. 1-66). American Mathematical Society
- (pp. 75-100). American Mathematical
Society
Conference proceedings papers
- (pp 75-100)
- (pp 1-21)
Preprints
- , arXiv.
- Resurgence and Riemann-Hilbert problems for elliptic Calabi-Yau threefolds, arXiv.
- .
- , arXiv.
- Complex hyperkähler structures defined by Donaldson-Thomas invariants, arXiv.
- On the monodromy of the deformed cubic oscillator, arXiv.
- Complex surfaces with equivalent derived categories, arXiv.
- A quantized Riemann-Hilbert problem in Donaldson-Thomas theory, 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.
- . 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
- , Simons Centre meeting, January 2021.
- , 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, 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 , April 2012.
- A video of an introductory lecture on derived categories in algebraic geometry, March 2007.
Links