Algebraic Geometry

Our research interests include complex geometry, arithmetic geometry, stability conditions, derived categories, moduli theory and birational geometry.

Staff

Publications

2024

Çanakçı, İ., King, A., Pressland, M. (2024) Perfect matching modules, dimer partition functions and cluster characters. Advances in Mathematics, 443, (doi: 10.1016/j.aim.2024.109570)

Dervan, R., McCarthy, J. B., Sektnan, L. M. (2024) Z-critical connections and Bridgeland stability conditions. Cambridge Journal of Mathematics,

2023

Nabijou, N., Wemyss, M. (2023) GV and GW invariants via the enhanced movable cone. Moduli,

Bellamy, G., Craw, A., Rayan, S., Schedler, T., Weiss, H. (2023) All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces. Journal of Algebraic Geometry,

Hirano, Y., Wemyss, M. (2023) Stability conditions for 3-fold flops. Duke Mathematical Journal, 172, pp. 3105-3173. (doi: 10.1215/00127094-2022-0097)

Bellamy, G., Thiel, U. (2023) The Rank One property for free Frobenius extensions. Comptes Rendus Mathématique, 361, pp. 1341-1348. (doi: 10.5802/crmath.502)

Hara, W., Wemyss, M. (2023) Spherical objects in dimension two and three. Journal of the European Mathematical Society,

Bellamy, G. (2023) Coulomb branches have symplectic singularities. Letters in Mathematical Physics, 113, (doi: 10.1007/s11005-023-01724-5)

Gvirtz-Chen, D., Mezzedimi, G. (2023) A Hilbert irreducibility theorem for Enriques surfaces. Transactions of the American Mathematical Society, 376, pp. 3867-3890. (doi: 10.1090/tran/8831)

Smith, I., Wemyss, M. (2023) Double bubble plumbings and two-curve flops. Selecta Mathematica - New Series, 29, (doi: 10.1007/s00029-023-00828-z)

Muthiah, D., Weekes, A. (2023) Feuilles symplectiques pour les tranches dans les Grassmanniennes affines généralisées = Symplectic leaves for generalized affine Grassmannian slices. Annales Scientifiques de l'École Normale Supérieure, 56, pp. 287-298. (doi: 10.24033/asens.2534)

Pressland, M. (2023) A categorification of acyclic principal coefficient cluster algebras. Nagoya Mathematical Journal, (doi: 10.1017/nmj.2023.6)

Dervan, R., Legendre, E. (2023) Valuative stability of polarised varieties. Mathematische Annalen, 385, pp. 357-391. (doi: 10.1007/s00208-021-02313-4)

Bellamy, G., Bonnafé, C., Fu, B., Juteau, D., Levy, P., Sommers, E. (2023) A new family of isolated symplectic singularities with trivial local fundamental group. Proceedings of the London Mathematical Society, (doi: 10.1112/plms.12513)

Bellamy, G., Schmitt, J., Thiel, U. (2023) On parabolic subgroups of symplectic reflection groups. Glasgow Mathematical Journal, (doi: 10.1017/S0017089522000416)

Dervan, R. (2023) Stability conditions for polarised varieties. Forum of Mathematics, Sigma, 11, (doi: 10.1017/fms.2023.104)

2022

Bellamy, G., Gunningham, S., Raskin, S. (2022) Projective generation for equivariant D-modules. Transformation Groups, 27, pp. 737-749. (doi: 10.1007/s00031-021-09660-1)

Bellamy, G., Thiel, U. (2022) Cellularity of endomorphism algebras of tilting objects. Advances in Mathematics, 404, (doi: 10.1016/j.aim.2022.108387)

Gvirtz, D., Skorobogatov, A. N. (2022) Cohomology and the Brauer groups of diagonal surfaces. Duke Mathematical Journal, 171, pp. 1299-1347. (doi: 10.1215/00127094-2021-0029)

Pressland, M., Sauter, J. (2022) On quiver Grassmannians and orbit closures for gen-finite modules. Algebras and Representation Theory, 25, pp. 413-445. (doi: 10.1007/s10468-021-10028-y)

Pressland, M., Sauter, J. (2022) Special tilting modules for algebras with positive dominant dimension. Glasgow Mathematical Journal, 64, pp. 79-105. (doi: 10.1017/S0017089520000609)

Pressland, M. (2022) Calabi–Yau properties of Postnikov diagrams. Forum of Mathematics, Sigma, 10, (doi: 10.1017/fms.2022.52)

Blakestad, C., Gvirtz, D., Heuer, B., Shchedrina, D., Shimizu, K., Wear, P., Yao, Z. (2022) Perfectoid covers of abelian varieties. Mathematical Research Letters, 29, pp. 631-662. (doi: 10.4310/mrl.2022.v29.n3.a2)

August, J., Wemyss, M. (2022) Stability conditions for contraction algebras. Forum of Mathematics, Sigma, 10, (doi: 10.1017/fms.2022.65)

2021

Donovan, W., Wemyss, M. (2021) Stringy Kähler moduli, mutation and monodromy. Journal of Differential Geometry,

Dervan, R., Sektnan, L. M. (2021) Optimal symplectic connections on holomorphic submersions. Communications on Pure and Applied Mathematics, 74, pp. 2132-2184. (doi: 10.1002/cpa.21930)

Dervan, R., Sektnan, L. M. (2021) Moduli theory, stability of fibrations and optimal symplectic connections. Geometry and Topology, 25, pp. 2643-2697. (doi: 10.2140/gt.2021.25.2643)

Bellamy, G., Brown, R., Cleland Woods, H., Labrosse, N., Senn, H., Singer, J., Vezza, M. (2021) Togetherness: the central tenet of an effective institutional online pivot. Journal of Perspectives in Applied Academic Practice, 9, pp. 82-90. (doi: 10.14297/jpaap.v9i2.491)

Muthiah, D. (2021) Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities. Advances in Mathematics, 385, (doi: 10.1016/j.aim.2021.107793)

Bellamy, G., Schedler, T. (2021) Symplectic resolutions of quiver varieties. Selecta Mathematica, 27, (doi: 10.1007/s00029-021-00647-0)

Bellamy, G., Boos, M. (2021) Semisimplicity of the category of admissible D-modules. Kyoto Journal of Mathematics, 61, pp. 115-170. (doi: 10.1215/21562261-2020-0006)

Dervan, R., Sektnan, L. M. (2021) Uniqueness of optimal symplectic connections. Forum of Mathematics, Sigma, 9, (doi: 10.1017/fms.2021.15)

Dervan, R., Sektnan, L. M. (2021) Hermitian Yang–Mills connections on blowups. Journal of Geometric Analysis, 31, pp. 516-542. (doi: 10.1007/s12220-019-00286-0)

Gvirtz, D., Loughran, D., Nakahara, M. (2021) Quantitative arithmetic of diagonal degree 2 K3 surfaces. Mathematische Annalen, 384, pp. 1-75. (doi: 10.1007/s00208-021-02280-w)

2020

Bellamy, G., Craw, A. (2020) Birational geometry of symplectic quotient singularities. Inventiones Mathematicae, 222, pp. 399-468. (doi: 10.1007/s00222-020-00972-9)

Muthiah, D., Weekes, A., Yacobi, O. (2020) On a conjecture of Pappas and Rapoport about the standard local model for GL_ d. Journal fur die Reine und Angewandte Mathematik (Crelles Journal), 772, pp. 175-185. (doi: 10.1515/crelle-2020-0030)

Muthiah, D., Puskás, A., Whitehead, I. (2020) Correction factors for Kac–Moody groups and t-deformed root multiplicities. Mathematische Zeitschrift, 296, pp. 127-145. (doi: 10.1007/s00209-019-02419-1)

Dao, H., Iyama, O., Takahashi, R., Wemyss, M. (2020) Gorenstein modifications and Q-Gorenstein rings. Journal of Algebraic Geometry, 29, pp. 729-751. (doi: 10.1090/jag/760)

Dervan, R. (2020) K-semistability of optimal degenerations. Quarterly Journal of Mathematics, 71, pp. 989-995. (doi: 10.1093/qmathj/haaa012)

Dervan, R., Székelyhidi, G. (2020) The Kähler–Ricci flow and optimal degenerations. Journal of Differential Geometry, 116, pp. 187-203. (doi: 10.4310/jdg/1599271255)

Muthiah, D., Weekes, A., Yacobi, O. (2020) The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman. International Mathematics Research Notices, 2022, pp. 1922-1972. (doi: 10.1093/imrn/rnaa131)

Dervan, R., Sektnan, L. M. (2020) Extremal metrics on fibrations. Proceedings of the London Mathematical Society, 120, pp. 587-616. (doi: 10.1112/plms.12297)

Pressland, M. (2020) Mutation of frozen Jacobian algebras. Journal of Algebra, 546, pp. 236-273. (doi: 10.1016/j.jalgebra.2019.10.035)

Bellamy, G., Boos, M. (2020) The (cyclic) enhanced nilpotent cone via quiver representations. Manuscripta Mathematica, 161, pp. 333-362. (doi: 10.1007/s00229-018-1098-9)

Iyama, O., Wemyss, M. (2020) Weighted projective lines and rational surface singularities. Épijournal de Géométrie Algébrique, 3,

2019

Bellamy, G. (2019) Rational Cherednik algebras and Schubert cells. Algebras and Representation Theory, 22, pp. 1533-1567. (doi: 10.1007/s10468-018-9831-3)

Dervan, R., Keller, J. (2019) A finite dimensional approach to Donaldson’s J‑flow. Communications in Analysis and Geometry, 27, pp. 1025-1085. (doi: 10.4310/CAG.2019.v27.n5.a2)

Bellamy, G., Schedler, T. (2019) On symplectic resolutions and factoriality of Hamiltonian reductions. Mathematische Annalen, 375, pp. 165-176. (doi: 10.1007/s00208-019-01851-2)

Dervan, R., Ross, J. (2019) Stable maps in higher dimensions. Mathematische Annalen, 374, pp. 1033-1073. (doi: 10.1007/s00208-018-1706-8)

Donovan, W., Wemyss, M. (2019) Contractions and deformations. American Journal of Mathematics, 141, pp. 563-592. (doi: 10.1353/ajm.2019.0018)

Muthiah, D., Orr, D. (2019) On the double-affine Bruhat order: the ε = 1 conjecture and classification of covers in ADE type. Algebraic Combinatorics, 2, pp. 197-216. (doi: 10.5802/alco.37)

Donovan, W., Wemyss, M. (2019) Noncommutative enhancements of contractions. Advances in Mathematics, 344, pp. 99-136. (doi: 10.1016/j.aim.2018.11.019)

Donovan, W., Wemyss, M. (2019) Twists and braids for general 3-fold flops. Journal of the European Mathematical Society, 21, pp. 1641-1701. (doi: 10.4171/JEMS/868)

Dao, H., Iyama, O., Iyengar, S. B., Takahashi, R., Wemyss, M., Yoshino, Y. (2019) Noncommutative resolutions using syzygies. Bulletin of the London Mathematical Society, 51, pp. 43-48. (doi: 10.1112/blms.12210)

2018

Dervan, R. (2018) Relative K-stability for Kähler manifolds. Mathematische Annalen, 372, pp. 859-889. (doi: 10.1007/s00208-017-1592-5)

Muthiah, D., Tingley, P. (2018) Affine PBW bases and affine MV polytopes. Selecta Mathematica - New Series, 24, pp. 4781-4810. (doi: 10.1007/s00029-018-0436-9)

Hirano, Y., Wemyss, M. (2018) Faithful actions from hyperplane arrangements. Geometry and Topology, 22, pp. 3395-3433. (doi: 10.2140/gt.2018.22.3395)

Kamnitzer, J., Muthiah, D., Weekes, A. (2018) On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian. Transformation Groups, 23, pp. 707-722. (doi: 10.1007/s00031-017-9455-4)

Brown, G., Wemyss, M. (2018) Gopakumar--Vafa invariants do not determine flops. Communications in Mathematical Physics, 361, pp. 143-154. (doi: 10.1007/s00220-017-3038-z)

Bellamy, G., Thiel, U. (2018) Highest weight theory for finite-dimensional graded algebras with triangular decomposition. Advances in Mathematics, 330, pp. 361-419. (doi: 10.1016/j.aim.2018.03.011)

Iyama, O., 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, pp. 149-202. (doi: 10.1515/crelle-2015-0031)

Bellamy, G., Schedler, T. (2018) Filtrations on Springer fiber cohomology and Kostka polynomials. Letters in Mathematical Physics, 108, pp. 679-698. (doi: 10.1007/s11005-017-1002-7)

Wemyss, M. (2018) Flops and clusters in the homological minimal model programme. Inventiones Mathematicae, 211, pp. 435-521. (doi: 10.1007/s00222-017-0750-4)

Muthiah, D. (2018) On Iwahori-Hecke algebras for p-adic loop groups: double coset basis and Bruhat order. American Journal of Mathematics, 140, pp. 221-244. (doi: 10.1353/ajm.2018.0004)

Kamnitzer, J., Muthiah, D., Weekes, A., Yacobi, O. (2018) Reducedness of affine Grassmannian slices in type A. Proceedings of the American Mathematical Society, 146, pp. 861-874. (doi: 10.1090/proc/13850)

Grabowski, J. E., Pressland, M. (2018) Graded Frobenius cluster categories. Documenta Mathematica, 23, pp. 49-76. (doi: 10.25537/DM.2018V23.49-76)

Bellamy, G., Schedler, T., Thiel, U. (2018) Hyperplane arrangements associated to symplectic quotient singularities. Banach Centre Publications, 116, pp. 25-45. (doi: 10.4064/bc116-2)

Muthiah, D., Orr, D. (2018) Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties. American Mathematical Society

2017

Pressland, M. (2017) Internally Calabi–Yau algebras and cluster-tilting objects. Mathematische Zeitschrift, 287, pp. 555-585. (doi: 10.1007/s00209-016-1837-0)

Dervan, R., Ross, J. (2017) K-stability for Kähler manifolds. Mathematical Research Letters, 24, pp. 689-739. (doi: 10.4310/MRL.2017.v24.n3.a5)

King, A., Pressland, M. (2017) Labelled seeds and the mutation group. Mathematical Proceedings of the Cambridge Philosophical Society, 163, pp. 193-217. (doi: 10.1017/s0305004116000918)

Bellamy, G., Dodd, C., McGerty, K., Nevins, T. (2017) Categorical cell decomposition of quantized symplectic algebraic varieties. Geometry and Topology, 21, pp. 2601-2681. (doi: 10.2140/gt.2017.21.2601)

Bellamy, G., Ginzburg, V. (2017) SL2-action on Hilbert Schemes and Calogero-Moser spaces. Michigan Mathematical Journal, 66, pp. 519-532. (doi: 10.1307/mmj/1496995337)

2016

Bellamy, G., Thiel, U. (2016) Cuspidal Calogero-Moser and Lusztig families for Coxeter groups. Journal of Algebra, 462, pp. 197-252. (doi: 10.1016/j.jalgebra.2016.06.003)

Dervan, R. (2016) Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, 25, pp. 919-934. (doi: 10.5802/afst.1515)

Dervan, R. (2016) On K-stability of finite covers. Bulletin of the London Mathematical Society, 48, pp. 717-728. (doi: 10.1112/blms/bdw029)

Codogni, G., Dervan, R. (2016) Non-reductive automorphism groups, the Loewy filtration and K-stability. Annales de l’institut Fourier, 66, pp. 1895-1921. (doi: 10.5802/aif.3052)

Bellamy, G. (2016) Counting resolutions of symplectic quotient singularities. Compositio Mathematica, 152, pp. 99-114. (doi: 10.1112/S0010437X15007630)

Bellamy, G., Rogalski, D., Schedler, T., Stafford, J. T., Wemyss, M. (2016) Noncommutative Algebraic Geometry. Cambridge University Press

Donovan, W., Wemyss, M. (2016) Noncommutative deformations and flops. Duke Mathematical Journal, 165, pp. 1397-1474. (doi: 10.1215/00127094-3449887)

Bellamy, G., Schedler, T. (2016) On the (non)existence of symplectic resolutions of linear quotients. Mathematical Research Letters, 23, pp. 1537-1564. (doi: 10.4310/MRL.2016.v23.n6.a1)

Dervan, R. (2016) Uniform stability of twisted constant scalar curvature Kähler metrics. International Mathematics Research Notices, 2016, pp. 4728-4783. (doi: 10.1093/imrn/rnv291)

2015

Kalck, M., Iyama, O., Wemyss, M., Yang, D. (2015) Frobenius categories, Gorenstein algebras and rational surface singularities. Compositio Mathematica, 151, pp. 502-534. (doi: 10.1112/S0010437X14007647)

Bellamy, G., Ginzburg, V. (2015) Hamiltonian reduction and nearby cycles for mirabolic D-modules. Advances in Mathematics, 269, pp. 71-161. (doi: 10.1016/j.aim.2014.10.002)

Postgraduate research students

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Algebraic Geometry - Example Research Projects

Our group has an active PhD student community, and every year we admit new PhD students. We welcome applications from across the world, and we encourage you to browse our available supervisors, and also to consult our general advice on how to navigate the application process.

Seminars

Regular seminars relevant to the group are held as part of the Algebraic Geometry seminar series. You can find a full list of the seminars within the school on the main seminars page, where you can subscribe to their respective calendars.

Algebraic geometry explores the geometry of spaces with an algebraic structure. The fundamental objects are algebraic varieties, which are the vanishing loci of polynomials. While algebraic geometry is one of the oldest and richest areas of pure mathematics, new tools from commutative algebra and differential geometry led to a revolution in the subject in the 20th century, and the area remains one of the most active and exciting areas of pure mathematics today.

The current research interests of the algebraic geometry group include homological algebra, complex geometry, arithmetic geometry, geometric representation theory, stability conditions, derived categories, moduli theory and birational geometry.

All information about our group, our members, our activities, and a full list of our expertise, can be found at Core Structures.

Our group has an active PhD student community, and every year we admit new PhD students.  We welcome applications from across the world, and we encourage you to browse our available supervisors, and also to consult our general advice on how to navigate the application process.