Professor Michael Wemyss
- The Chair of Mathematics (Mathematics)
telephone:
0141 330 3314
email:
Michael.Wemyss@glasgow.ac.uk
Office 435, Mathematics and Statistics Building, University Place, Glasgow, G12 8QQ
https://orcid.org/0000-0003-4760-7750Research interests
Algebraic geometry and its interactions, principally between noncommutative and homological algebra, resolutions of singularities, and the minimal model program. All related structures, including: deformation theory, derived categories, stability conditions, associated commutative and homological structures and their representation theory, curve invariants, McKay correspondence, Cohen--Macaulay modules, finite dimensional algebras and cluster-tilting theory.
Research groups
Publications
Selected publications
Wemyss, M. (2018) Flops and clusters in the homological minimal model programme. Inventiones Mathematicae, 211(2), pp. 435-521. (doi: 10.1007/s00222-017-0750-4)
Iyama, O. and Wemyss, M. (2014) Maximal modifications and Auslander–Reiten duality for non-isolated singularities. Inventiones Mathematicae, 197(3), pp. 521-586. (doi: 10.1007/s00222-013-0491-y)
Donovan, W. and Wemyss, M. (2016) Noncommutative deformations and flops. Duke Mathematical Journal, 165(8), pp. 1397-1474. (doi: 10.1215/00127094-3449887)
Hirano, Y. and Wemyss, M. (2023) Stability conditions for 3-fold flops. Duke Mathematical Journal, 172(16), pp. 3105-3173. (doi: 10.1215/00127094-2022-0097)
Donovan, W. and Wemyss, M. (2019) Twists and braids for general 3-fold flops. Journal of the European Mathematical Society, 21(6), pp. 1641-1701. (doi: 10.4171/JEMS/868)
Wemyss, M. (2011) The GL(2, C) McKay correspondence. Mathematische Annalen, 350(3), pp. 631-659. (doi: 10.1007/s00208-010-0572-9)
Iyama, O. and Wemyss, M. (2013) On the noncommutative Bondal–Orlov conjecture. Journal für die reine und angewandte Mathematik (Crelles Journal), 683, pp. 119-128. (doi: 10.1515/crelle-2012-0001)
Hirano, Y. and Wemyss, M. (2018) Faithful actions from hyperplane arrangements. Geometry and Topology, 22(6), pp. 3395-3433. (doi: 10.2140/gt.2018.22.3395)
Donovan, W. and Wemyss, M. (2019) Contractions and deformations. American Journal of Mathematics, 141(3), pp. 563-592. (doi: 10.1353/ajm.2019.0018)
All publications
2025
Brown, G. and Wemyss, M. (2025) Local normal forms of noncommutative functions. Forum of Mathematics, Pi, (Accepted for Publication)
Donovan, W. and Wemyss, M. (2025) Stringy Kähler moduli, mutation and monodromy. Journal of Differential Geometry, 129(1), pp. 115-164. (doi: 10.4310/jdg/1736262124)
2024
Brown, G. and Wemyss, M. (2024) Derived deformation theory of crepant curves. Journal of Topology, 17(4), e12359. (doi: 10.1112/topo.12359)
Hara, W. and Wemyss, M. (2024) Spherical objects in dimension two and three. Journal of the European Mathematical Society, (doi: 10.4171/JEMS/1504) (Early Online Publication)
Nabijou, N. and Wemyss, M. (2024) GV and GW invariants via the enhanced movable cone. Moduli, 1, e8. (doi: 10.1112/mod.2024.4)
2023
Hirano, Y. and Wemyss, M. (2023) Stability conditions for 3-fold flops. Duke Mathematical Journal, 172(16), pp. 3105-3173. (doi: 10.1215/00127094-2022-0097)
Smith, I. and Wemyss, M. (2023) Double bubble plumbings and two-curve flops. Selecta Mathematica - New Series, 29(2), 29. (doi: 10.1007/s00029-023-00828-z)
2022
August, J. and Wemyss, M. (2022) Stability conditions for contraction algebras. Forum of Mathematics, Sigma, 10, e73. (doi: 10.1017/fms.2022.65)
2020
Dao, H., Iyama, O., Takahashi, R. and Wemyss, M. (2020) Gorenstein modifications and Q-Gorenstein rings. Journal of Algebraic Geometry, 29(4), pp. 729-751. (doi: 10.1090/jag/760)
Iyama, O. and Wemyss, M. (2020) Weighted projective lines and rational surface singularities. Épijournal de Géométrie Algébrique, 3, 13.
2019
Donovan, W. and Wemyss, M. (2019) Contractions and deformations. American Journal of Mathematics, 141(3), pp. 563-592. (doi: 10.1353/ajm.2019.0018)
Donovan, W. and Wemyss, M. (2019) Noncommutative enhancements of contractions. Advances in Mathematics, 344, pp. 99-136. (doi: 10.1016/j.aim.2018.11.019)
Donovan, W. and Wemyss, M. (2019) Twists and braids for general 3-fold flops. Journal of the European Mathematical Society, 21(6), pp. 1641-1701. (doi: 10.4171/JEMS/868)
Dao, H., Iyama, O., Iyengar, S. B., Takahashi, R., Wemyss, M. and Yoshino, Y. (2019) Noncommutative resolutions using syzygies. Bulletin of the London Mathematical Society, 51(1), pp. 43-48. (doi: 10.1112/blms.12210)
2018
Hirano, Y. and Wemyss, M. (2018) Faithful actions from hyperplane arrangements. Geometry and Topology, 22(6), pp. 3395-3433. (doi: 10.2140/gt.2018.22.3395)
Brown, G. and Wemyss, M. (2018) Gopakumar--Vafa invariants do not determine flops. Communications in Mathematical Physics, 361(1), pp. 143-154. (doi: 10.1007/s00220-017-3038-z)
Iyama, O. and Wemyss, M. (2018) Reduction of triangulated categories and Maximal Modification Algebras for cA_n singularities. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 2018(738), pp. 149-202. (doi: 10.1515/crelle-2015-0031)
Wemyss, M. (2018) Flops and clusters in the homological minimal model programme. Inventiones Mathematicae, 211(2), pp. 435-521. (doi: 10.1007/s00222-017-0750-4)
2016
Bellamy, G. , Rogalski, D., Schedler, T., Stafford, J. T. and Wemyss, M. (2016) Noncommutative Algebraic Geometry. Series: Mathematical Sciences Research Institute publications, 64. Cambridge University Press. ISBN 9781107129542
Donovan, W. and Wemyss, M. (2016) Noncommutative deformations and flops. Duke Mathematical Journal, 165(8), pp. 1397-1474. (doi: 10.1215/00127094-3449887)
2015
Kalck, M., Iyama, O., Wemyss, M. and Yang, D. (2015) Frobenius categories, Gorenstein algebras and rational surface singularities. Compositio Mathematica, 151(3), pp. 502-534. (doi: 10.1112/S0010437X14007647)
2014
Iyama, O. and Wemyss, M. (2014) Maximal modifications and Auslander–Reiten duality for non-isolated singularities. Inventiones Mathematicae, 197(3), pp. 521-586. (doi: 10.1007/s00222-013-0491-y)
Iyama, O. and Wemyss, M. (2014) Singular derived categories of -factorial terminalizations and maximal modification algebras. Advances in Mathematics, 261, pp. 85-121. (doi: 10.1016/j.aim.2014.04.001)
2013
Iyama, O. and Wemyss, M. (2013) On the noncommutative Bondal–Orlov conjecture. Journal für die reine und angewandte Mathematik (Crelles Journal), 683, pp. 119-128. (doi: 10.1515/crelle-2012-0001)
Wemyss, M. (2013) Reconstruction algebras of type D (II). Hokkaido Mathematical Journal, 42(2), pp. 293-329. (doi: 10.14492/hokmj/1372859589)
2012
Wemyss, M. (2012) Reconstruction algebras of type D (I). Journal of Algebra, 356(1), pp. 158-194. (doi: 10.1016/j.jalgebra.2012.01.019)
2011
Wemyss, M. (2011) The GL(2, C) McKay correspondence. Mathematische Annalen, 350(3), pp. 631-659. (doi: 10.1007/s00208-010-0572-9)
Wemyss, M. (2011) Reconstruction algebras of type A. Transactions of the American Mathematical Society, 363(6), pp. 3101-3132. (doi: 10.1090/S0002-9947-2011-05130-5)
Iyama, O. and Wemyss, M. (2011) A new triangulated category for rational surface singularities. Illinois Journal of Mathematics, 55(1), pp. 325-341.
2010
Bocklandt, R., Schedler, T. and Wemyss, M. (2010) Superpotentials and higher order derivations. Journal of Pure and Applied Algebra, 214(9), pp. 1501-1522. (doi: 10.1016/j.jpaa.2009.07.013)
Iyama, O. and Wemyss, M. (2010) The classification of special Cohen–Macaulay modules. Mathematische Zeitschrift, 265(1), pp. 41-83. (doi: 10.1007/s00209-009-0501-3)
Articles
Brown, G. and Wemyss, M. (2025) Local normal forms of noncommutative functions. Forum of Mathematics, Pi, (Accepted for Publication)
Donovan, W. and Wemyss, M. (2025) Stringy Kähler moduli, mutation and monodromy. Journal of Differential Geometry, 129(1), pp. 115-164. (doi: 10.4310/jdg/1736262124)
Brown, G. and Wemyss, M. (2024) Derived deformation theory of crepant curves. Journal of Topology, 17(4), e12359. (doi: 10.1112/topo.12359)
Hara, W. and Wemyss, M. (2024) Spherical objects in dimension two and three. Journal of the European Mathematical Society, (doi: 10.4171/JEMS/1504) (Early Online Publication)
Nabijou, N. and Wemyss, M. (2024) GV and GW invariants via the enhanced movable cone. Moduli, 1, e8. (doi: 10.1112/mod.2024.4)
Hirano, Y. and Wemyss, M. (2023) Stability conditions for 3-fold flops. Duke Mathematical Journal, 172(16), pp. 3105-3173. (doi: 10.1215/00127094-2022-0097)
Smith, I. and Wemyss, M. (2023) Double bubble plumbings and two-curve flops. Selecta Mathematica - New Series, 29(2), 29. (doi: 10.1007/s00029-023-00828-z)
August, J. and Wemyss, M. (2022) Stability conditions for contraction algebras. Forum of Mathematics, Sigma, 10, e73. (doi: 10.1017/fms.2022.65)
Dao, H., Iyama, O., Takahashi, R. and Wemyss, M. (2020) Gorenstein modifications and Q-Gorenstein rings. Journal of Algebraic Geometry, 29(4), pp. 729-751. (doi: 10.1090/jag/760)
Iyama, O. and Wemyss, M. (2020) Weighted projective lines and rational surface singularities. Épijournal de Géométrie Algébrique, 3, 13.
Donovan, W. and Wemyss, M. (2019) Contractions and deformations. American Journal of Mathematics, 141(3), pp. 563-592. (doi: 10.1353/ajm.2019.0018)
Donovan, W. and Wemyss, M. (2019) Noncommutative enhancements of contractions. Advances in Mathematics, 344, pp. 99-136. (doi: 10.1016/j.aim.2018.11.019)
Donovan, W. and Wemyss, M. (2019) Twists and braids for general 3-fold flops. Journal of the European Mathematical Society, 21(6), pp. 1641-1701. (doi: 10.4171/JEMS/868)
Dao, H., Iyama, O., Iyengar, S. B., Takahashi, R., Wemyss, M. and Yoshino, Y. (2019) Noncommutative resolutions using syzygies. Bulletin of the London Mathematical Society, 51(1), pp. 43-48. (doi: 10.1112/blms.12210)
Hirano, Y. and Wemyss, M. (2018) Faithful actions from hyperplane arrangements. Geometry and Topology, 22(6), pp. 3395-3433. (doi: 10.2140/gt.2018.22.3395)
Brown, G. and Wemyss, M. (2018) Gopakumar--Vafa invariants do not determine flops. Communications in Mathematical Physics, 361(1), pp. 143-154. (doi: 10.1007/s00220-017-3038-z)
Iyama, O. and Wemyss, M. (2018) Reduction of triangulated categories and Maximal Modification Algebras for cA_n singularities. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 2018(738), pp. 149-202. (doi: 10.1515/crelle-2015-0031)
Wemyss, M. (2018) Flops and clusters in the homological minimal model programme. Inventiones Mathematicae, 211(2), pp. 435-521. (doi: 10.1007/s00222-017-0750-4)
Donovan, W. and Wemyss, M. (2016) Noncommutative deformations and flops. Duke Mathematical Journal, 165(8), pp. 1397-1474. (doi: 10.1215/00127094-3449887)
Kalck, M., Iyama, O., Wemyss, M. and Yang, D. (2015) Frobenius categories, Gorenstein algebras and rational surface singularities. Compositio Mathematica, 151(3), pp. 502-534. (doi: 10.1112/S0010437X14007647)
Iyama, O. and Wemyss, M. (2014) Maximal modifications and Auslander–Reiten duality for non-isolated singularities. Inventiones Mathematicae, 197(3), pp. 521-586. (doi: 10.1007/s00222-013-0491-y)
Iyama, O. and Wemyss, M. (2014) Singular derived categories of -factorial terminalizations and maximal modification algebras. Advances in Mathematics, 261, pp. 85-121. (doi: 10.1016/j.aim.2014.04.001)
Iyama, O. and Wemyss, M. (2013) On the noncommutative Bondal–Orlov conjecture. Journal für die reine und angewandte Mathematik (Crelles Journal), 683, pp. 119-128. (doi: 10.1515/crelle-2012-0001)
Wemyss, M. (2013) Reconstruction algebras of type D (II). Hokkaido Mathematical Journal, 42(2), pp. 293-329. (doi: 10.14492/hokmj/1372859589)
Wemyss, M. (2012) Reconstruction algebras of type D (I). Journal of Algebra, 356(1), pp. 158-194. (doi: 10.1016/j.jalgebra.2012.01.019)
Wemyss, M. (2011) The GL(2, C) McKay correspondence. Mathematische Annalen, 350(3), pp. 631-659. (doi: 10.1007/s00208-010-0572-9)
Wemyss, M. (2011) Reconstruction algebras of type A. Transactions of the American Mathematical Society, 363(6), pp. 3101-3132. (doi: 10.1090/S0002-9947-2011-05130-5)
Iyama, O. and Wemyss, M. (2011) A new triangulated category for rational surface singularities. Illinois Journal of Mathematics, 55(1), pp. 325-341.
Bocklandt, R., Schedler, T. and Wemyss, M. (2010) Superpotentials and higher order derivations. Journal of Pure and Applied Algebra, 214(9), pp. 1501-1522. (doi: 10.1016/j.jpaa.2009.07.013)
Iyama, O. and Wemyss, M. (2010) The classification of special Cohen–Macaulay modules. Mathematische Zeitschrift, 265(1), pp. 41-83. (doi: 10.1007/s00209-009-0501-3)
Books
Bellamy, G. , Rogalski, D., Schedler, T., Stafford, J. T. and Wemyss, M. (2016) Noncommutative Algebraic Geometry. Series: Mathematical Sciences Research Institute publications, 64. Cambridge University Press. ISBN 9781107129542
Grants
Current:
- ERC Consolidator Grant, 2021-26.
- EPSRC Programme Grant "Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations", 2018-24.
- GRAID Programme for PhD supervision in Uganda, 2019-2022, joint with David Ssevviiri.
Supervision
I currently advise PhD students Caro, Brian, Sam, Zhang, Charlotte, Marina and Parth.
I am always interested in hearing from potential PhD students and postdocs, so feel free to contact me directly, or see the up-date information about supervision opportunities for both me and the wider group at our available supervisors page, and our positions page.
- Shimpi, Parth Anil
Topological Aspects of Noncommutative Resolutions
Professional activities & recognition
Prizes, awards & distinctions
- 2017: LMS Whitehead Prize (LMS)
- 2020: Adams Prize (Cambridge University)
Research fellowships
- 2013 - 2021: EPSRC Early Career Fellowship, with 3 year extension
Grant committees & research advisory boards
- 2021: REF, Member, REF2021 Sub-panel 10: Mathematical Sciences
Professional & learned societies
- Chair, Glasgow Mathematical Journal Trust
- Chair, joint BMC/BAMC conference, Glasgow 2021
