Algebra

Our research interests include geometric group theory, representation theory and geometric representation theory.

Staff

Publications

2024

Bruce, C., Li, X. (2024) Algebraic actions I. C*-algebras and groupoids. Journal of Functional Analysis, 286, (doi: 10.1016/j.jfa.2023.110263)

Canakci, I., King, A., Pressland, M. (2024) Perfect matching modules, dimer partition functions and cluster characters. Advances in Mathematics,

Daws, M., Krajczok, J., Voigt, C. (2024) The approximation property for locally compact quantum groups. Advances in Mathematics, 438, (doi: 10.1016/j.aim.2023.109452)

2023

Boyd, R., Hepworth, R., Patzt, P. (2023) The homology of the partition algebras. Pacific Journal of Mathematics,

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

Azemar, A., Gadre, V. (2023) Stationary measures on the circle from hyperbolic surfaces with cusps cannot be straightened by quasi-symmetries. arXiv, (doi: 10.48550/arXiv.2311.09973)

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,

Brendle, T., Broaddus, N., Putman, A. (2023) The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary. Israel Journal of Mathematics, (doi: 10.1007/s11856-023-2566-9)

Brown, K., Carvalho, P. A.A.B., Matczuk, J. (2023) Critical and injective modules over skew polynomial rings. Journal of Pure and Applied Algebra, 227, (doi: 10.1016/j.jpaa.2023.107441)

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,

Boyd, R., Kastenholz, T., Mutanguha, J. P. (2023) The minimal genus problem for right angled Artin groups. Geometriae Dedicata, 217, (doi: 10.1007/s10711-023-00815-w)

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

Li, X., Raad, A. I. (2023) Constructing C*-diagonals in AH-algebras. Transactions of the American Mathematical Society, (doi: 10.1090/tran/9023)

Boyd, R., Charney, R., Morris-Wright, R., Rees, S. (2023) The Artin monoid Cayley graph. Journal of Combinatorial Algebra,

Kakariadis, E. T.A., Katsoulis, E. G., Laca, M., Li, X. (2023) Couniversality and controlled maps on product systems over right LCM semigroups. Analysis and PDE, 16, pp. 1433-1483. (doi: 10.2140/apde.2023.16.1433)

Gadre, V., Hensel, S. (2023) Linear progress in fibres. Groups, Geometry and Dynamics,

Kakariadis, E. T.A., Katsoulis, E. G., Li, X. (2023) Stable isomorphisms of operator algebras. International Mathematics Research Notices, (doi: 10.1093/imrn/rnad146)

Azemar, A., Gadre, V., Gouëzel, S., Haettel, T., Lessa, P., Uyanik, C. (2023) Random walk speed is a proper function on Teichmüller space. Journal of Modern Dynamics, 19, pp. 815-832. (doi: 10.3934/jmd.2023022)

Bell, J. P., Brown, K., Nazemian, Z., Smertnig, D. (2023) On noncommutative bounded factorization domains and prime rings. Journal of Algebra, 622, pp. 404-449. (doi: 10.1016/j.jalgebra.2023.01.023)

Li, X. (2023) Left regular representations of Garside categories I. C*-algebras and groupoids. Glasgow Mathematical Journal, 65, pp. S53-S86. (doi: 10.1017/S0017089522000106)

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

Brendle, T., Broaddus, N., Putman, A. (2023) The mapping class group of connect sums of S2 x S1. Transactions of the American Mathematical Society, 376, pp. 2557-2572. (doi: 10.1090/tran/8758)

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)

Skalski, A., Vergnioux, R., Voigt, C. (2023) Hecke algebras and the Schlichting completion for discrete quantum groups. Journal of the London Mathematical Society, 107, pp. 843-885. (doi: 10.1112/jlms.12701)

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

Voigt, C. (2023) Infinite quantum permutations. Advances in Mathematics, 415, (doi: 10.1016/j.aim.2023.108887)

Bruce, C., Li, X. (2023) On K-theoretic invariants of semigroup C*-algebras from actions of congruence monoids. American Journal of Mathematics, 145, pp. 251-285. (doi: 10.1353/ajm.2023.0005)

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)

Brown, K.A., Couto, M., Jahn, A. (2023) The finite dual of commutative-by-finite Hopf algebras. Glasgow Mathematical Journal, 65, pp. 62-89. (doi: 10.1017/S0017089522000052)

Gadre, V. (2023) Weil--Petersson geodesics on the modular surface. Mathematische Zeitschrift, 303, (doi: 10.1007/s00209-022-03171-9)

Chen, C., Li, X. (2023) Semigroup C*-algebras arising from graphs of monoids. International Mathematics Research Notices, (doi: 10.1093/imrn/rnac332)

Voigt, C., Yuncken, R. (2023) The Plancherel formula for complex semisimple quantum groups. Annales Scientifiques de l'École Normale Supérieure, 56, pp. 299-322. (doi: 10.24033/asens.2535)

Boyd, R., Hepworth, R. (2023) The homology of the Temperley-Lieb algebras. Geometry and Topology,

2022

Baker, A. (2022) Endotrivial modules for the quaternion group and iterated Jokers in chromatic homotopy theory. arXiv, (doi: 10.48550/arXiv.2212.00437)

Baker, A. (2022) Locally Frobenius algebras and Hopf algebras.

Baker, A. (2022) On P-algebras and their duals.

Feigin, M., Vrabec, M. (2022) Bispectrality of AG2 Calogero–Moser–Sutherland system. Mathematical Physics, Analysis and Geometry, 25, (doi: 10.1007/s11040-022-09440-7)

Li, X. (2022) Constructing Menger manifold C*-diagonals in classifiable C*-algebras. International Mathematics Research Notices, 2022, pp. 18992-19053. (doi: 10.1093/imrn/rnab199)

Hirano, Y., Wemyss, M. (2022) Stability conditions for 3-fold flops. Duke Mathematical Journal,

Boyd, R., Charney, R., Morris-Wright, R. (2022) A Deligne complex for Artin monoids. Journal of Algebra, 607, pp. 53-78. (doi: 10.1016/j.jalgebra.2021.03.015)

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)

Brown, K., Tabiri, A. A. (2022) Plane curves which are quantum homogenous spaces. Algebras and Representation Theory, 25, pp. 889-922. (doi: 10.1007/s10468-021-10052-y)

Voigt, C. (2022) On the assembly map for complex semisimple quantum groups. International Mathematics Research Notices, 2022, pp. 9603-9632. (doi: 10.1093/imrn/rnaa370)

Feigin, M., Hakobyan, T. (2022) Algebra of Dunkl Laplace–Runge–Lenz vector. Letters in Mathematical Physics, 112, (doi: 10.1007/s11005-022-01551-0)

Kakariadis, E. T.A., Katsoulis, E. G., Laca, M., Li, X. (2022) Boundary quotient C*-algebras of semigroups. Journal of the London Mathematical Society, 105, pp. 2136-2166. (doi: 10.1112/jlms.12557)

Dor-On, A., Kakariadis, E.T.A., Katsoulis, E., Laca, M., Li, X. (2022) C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems. Advances in Mathematics, 400, (doi: 10.1016/j.aim.2022.108286)

Gadre, V., Matheus, C. (2022) Cusp excursions of random geodesics in Weil-Petersson type metrics. Journal of Differential Geometry, 121, pp. 31-55. (doi: 10.4310/jdg/1656005495)

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)

Azemar, A., Gadre, V., Jeffreys, L. (2022) Statistical hyperbolicity for harmonic measure. International Mathematics Research Notices, 2022, pp. 6289-6309. (doi: 10.1093/imrn/rnaa277)

Li, X. (2022) K-theory for semigroup C*-algebras and partial crossed products. Communications in Mathematical Physics, 390, pp. 1-32. (doi: 10.1007/s00220-021-04194-9)

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)

Brown, K. A., Zhang, J. J. (2022) Iterated Hopf Ore extensions in positive characteristic. Journal of Noncommutative Geometry, 16, pp. 787-837. (doi: 10.4171/jncg/453)

Brannan, M., Eifler, K., Voigt, C., Weber, M. (2022) Quantum Cuntz-Krieger algebras. Transactions of the American Mathematical Society, 9, pp. 782-826. (doi: 10.1090/btran/88)

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,

Gadre, V. (2021) Trimmed sums of twists and the area Siegel-Veech constant. Manuscripta Mathematica, 166, pp. 91-99. (doi: 10.1007/s00229-020-01226-x)

Boyd, R., Hepworth, R., Patzt, P. (2021) The homology of the Brauer algebras. Selecta Mathematica, 27, (doi: 10.1007/s00029-021-00697-4)

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)

Boyd, R., Hepworth, R. (2021) Combinatorics of injective words for Temperley-Lieb algebras. Journal of Combinatorial Theory, Series A, 181, (doi: 10.1016/j.jcta.2021.105446)

Feigin, M. V., Hallnäs, M. A., Veselov, A. P. (2021) Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence. Communications in Mathematical Physics, 386, pp. 107-141. (doi: 10.1007/s00220-021-04036-8)

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)

Brown, K.A., Zhang, J.J. (2021) Survey on Hopf algebras of GK-dimension 1 and 2. Contemporary Mathematics, 771, pp. 43-62. (doi: 10.1090/conm/771/15507)

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)

Baker, A. (2021) On the dual of a P-algebra and its comodules, with applications to comparison of some Bousfield classes.

Li, X., Omland, T., Spielberg, J. (2021) C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type. Communications in Mathematical Physics, 381, pp. 1263-1308. (doi: 10.1007/s00220-020-03758-5)

Bell, M., Delecroix, V., Gadre, V., Gutiérrez-Romo, R., Schleimer, S. (2021) The flow group of rooted abelian or quadratic differentials. arXiv,

Korff, C. (2021) Cylindric Hecke characters and Gromov-Witten invariants via the asymmetric six-vertex model. Communications in Mathematical Physics, 381, pp. 591-640. (doi: 10.1007/s00220-020-03906-x)

2020

Alkadhem, M., Feigin, M. (2020) Trigonometric V-systems and solutions of WDVV equations. Journal of Physics A: Mathematical and Theoretical, 54, (doi: 10.1088/1751-8121/abccf8)

Boyd, R. (2020) The low-dimensional homology of finite-rank Coxeter groups. Algebraic and Geometric Topology, 20, pp. 2609-2655. (doi: 10.2140/agt.2020.20.2609)

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

Antoun, J., Voigt, C. (2020) On bicolimits of C*-categories. Theory and Applications of Categories, 35, pp. 1683-1725.

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)

Gorbounov, V.G., Korff, C., Stroppel, C. (2020) Yang-Baxter algebras, convolution algebras, and Grassmannians. Russian Mathematical Surveys, 75, (doi: 10.1070/RM9959)

Barlak, S., Li, X. (2020) Cartan subalgebras and the UCT problem, II. Mathematische Annalen, 378, pp. 255-287. (doi: 10.1007/s00208-020-02022-4)

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)

Bartel, A., Lenstra Jr., H. W. (2020) On class groups of random number fields. Proceedings of the London Mathematical Society, 121, pp. 927-953. (doi: 10.1112/plms.12343)

Voigt, C., Yuncken, R. (2020) Complex Semisimple Quantum Groups and Representation Theory. Springer

Boyd, R. (2020) Homological stability for Artin monoids. Proceedings of the London Mathematical Society, 121, pp. 537-583. (doi: 10.1112/plms.12335)

Gadre, V., Maher, J. (2020) Recurrence of quadratic differentials for harmonic measure. Mathematical Proceedings of the Cambridge Philosophical Society, 169, pp. 299-305. (doi: 10.1017/S0305004119000185)

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)

Alkadhem, M., Antoniou, G., Feigin, M. (2020) Solutions of BCn type of WDVV equations. American Mathematical Society

Baker, A. (2020) Homotopy theory of modules over a commutative $S-algebra: some tools and examples. arXiv,

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)

Korff, C., Palazzo, D. (2020) Cylindric symmetric functions and positivity. Algebraic Combinatorics, 3, pp. 191-247. (doi: 10.5802/alco.90)

Li, X. (2020) Every classifiable simple C*-algebra has a Cartan subalgebra. Inventiones Mathematicae, 219, pp. 653-699. (doi: 10.1007/s00222-019-00914-0)

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

Baker, A. (2020) Power operations in K-theory completed at a prime. Tbilisi Mathematical Journal, pp. 33-49.

Baker, A., Bauer, T. (2020) The realizability of some finite-length modules over the Steenrod algebra by spaces. Algebraic and Geometric Topology, 20, pp. 2129-2143. (doi: 10.2140/agt.2020.20.2129)

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)

Li, X. (2019) K-theory for generalized Lamplighter groups. Proceedings of the American Mathematical Society, 147, pp. 4371-4378. (doi: 10.1090/proc/14619)

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)

Bell, M., Delecroix, V., Gadre, V., Gutierrez-Romo, R., Schleimer, S. (2019) Coding Teichmuller flow using veering triangulations. arXiv,

Li, X., Renault, J. (2019) Cartan subalgebras in C*-algebras. Existence and uniqueness. Transactions of the American Mathematical Society, 372, pp. 1985-2010. (doi: 10.1090/tran/7654)

Feigin, M., Vrabec, M. (2019) Intertwining operator for AG2 Calogero-Moser-Sutherland system. Journal of Mathematical Physics, 60, (doi: 10.1063/1.5090274)

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

Cornelissen, G., Li, X., Marcolli, M., Smit, H. (2019) Reconstructing global fields from dynamics in the abelianized Galois group. Selecta Mathematica - New Series, 25, (doi: 10.1007/s00029-019-0469-8)

Bartel, A., Spencer, M. (2019) Relations between permutation representations in positive characteristic. Bulletin of the London Mathematical Society, 51, pp. 293-308. (doi: 10.1112/blms.12230)

Brown, K., Carvalho, P. A.A.B., Matczuk, J. (2019) Simple modules and their essential extensions for skew polynomial rings. Mathematische Zeitschrift, 291, pp. 877-903. (doi: 10.1007/s00209-018-2128-8)

Cornelissen, G., de Smit, B., Li, X., Marcolli, M., Smit, H. (2019) Characterization of global fields by Dirichlet L-series. Research in Number Theory, 5, (doi: 10.1007/s40993-018-0143-9)

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)

Antoniou, G., Feigin, M. (2019) Supersymmetric V-systems. Journal of High Energy Physics, 2019, (doi: 10.1007/JHEP02(2019)115)

Monk, A., Voigt, C. (2019) Complex quantum groups and a deformation of the Baum-Connes assembly map. Transactions of the American Mathematical Society, 371, pp. 8849-8877. (doi: 10.1090/tran/7774)

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)

Brown, K.A., Gilmartin, P., Zhang, J.J. (2019) Connected (graded) Hopf algebras. Transactions of the American Mathematical Society, 372, pp. 3283-3317. (doi: 10.1090/tran/7686)

Bartel, A., Page, A. (2019) Group representations in the homology of 3-manifolds. Commentarii Mathematici Helvetici, 94, pp. 67-88. (doi: 10.4171/CMH/455)

Brendle, T. E., Margalit, D. (2019) Normal subgroups of mapping class groups and the metaconjecture of Ivanov. Journal of the American Mathematical Society, 32, pp. 1009-1070. (doi: 10.1090/jams/927)

2018

Brown, K.A., Yakimov, M.T. (2018) Azumaya loci and discriminant ideals of PI algebras. Advances in Mathematics, 340, pp. 1219-1255. (doi: 10.1016/j.aim.2018.10.024)

Brendle, T., Margalit, D. (2018) Erratum to: Commensurations of the Johnson kernel. Geometry and Topology, (doi: 10.2140/gt.2004.8.1361)

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)

Gadre, V., Maher, J. (2018) The stratum of random mapping classes. Ergodic Theory and Dynamical Systems, 38, pp. 2666-2682. (doi: 10.1017/etds.2016.132)

Brown, K. A., Zhang, J. J. (2018) Unimodular graded Poisson Hopf algebras. Bulletin of the London Mathematical Society, 50, pp. 887-898. (doi: 10.1112/blms.12194)

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)

Baker, A. (2018) Iterated doubles of the Joker and their realisability. Homology, Homotopy and Applications, 20, pp. 341-360. (doi: 10.4310/HHA.2018.v20.n2.a17)

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)

Chu, C.-H., Li, X. (2018) Amenability, Reiter's condition and Liouville property. Journal of Functional Analysis, 274, pp. 3291-3324. (doi: 10.1016/j.jfa.2018.03.014)

Li, X. (2018) Continuous orbit equivalence rigidity. Ergodic Theory and Dynamical Systems, 38, pp. 1543-1563. (doi: 10.1017/etds.2016.98)

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)

Feigin, M. V., Veselov, A. P. (2018) ∨-systems, holonomy lie algebras, and logarithmic vector fields. International Mathematics Research Notices, 2018, pp. 2070-2098. (doi: 10.1093/imrn/rnw289)

Korff, C., Palazzo, D. (2018) Cylindric reverse plane partitions and 2D TQFT. Séminaire Lotharingien de Combinatoire, 80B,

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)

Baker, A. (2018) Characteristics for E∞ ring spectra. Contemporary Mathematics, 708, pp. 1-17. (doi: 10.1090/conm/708)

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)

Brendle, T. E., Margalit, D. (2018) The level four braid group. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 735, pp. 249-264. (doi: 10.1515/crelle-2015-0032)

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

2017

Brown, K. A., Macleod, M. J. (2017) The Cohen Macaulay property for noncommutative rings. Algebras and Representation Theory, 20, pp. 1433-1465. (doi: 10.1007/s10468-017-9694-z)

Voigt, C. (2017) On the structure of quantum automorphism groups. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 732, pp. 255-273. (doi: 10.1515/crelle-2014-0141)

(2017) K-Theory for Group C*-Algebras and Semigroup C*-Algebras. 47, (doi: 10.1007/978-3-319-59915-1)

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

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)

Li, X. (2017) Partial transformation groupoids attached to graphs and semigroups. International Mathematics Research Notices, 2017, pp. 5233-5259. (doi: 10.1093/imrn/rnw166)

Barlak, S., Li, X. (2017) Cartan subalgebras and the UCT problem. Advances in Mathematics, 316, pp. 748-769. (doi: 10.1016/j.aim.2017.06.024)

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)

Bartel, A., Spencer, M. (2017) A note on Green functors with inflation. Journal of Algebra, 483, pp. 230-244. (doi: 10.1016/j.jalgebra.2017.03.031)

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)

Brendle, T., Childers, L., Margalit, D. (2017) Mapping class groups. Princeton University Press

Gorbounov, V., Korff, C. (2017) Quantum integrability and generalised quantum Schubert calculus. Advances in Mathematics, 313, pp. 282-356. (doi: 10.1016/j.aim.2017.03.030)

Baker, A. (2017) E∞ ring spectra and elements of Hopf invariant 1. Boletín de la Sociedad Matemática Mexicana, 23, pp. 195-231. (doi: 10.1007/s40590-016-0096-8)

Barlak, S., Szabo, G., Voigt, C. (2017) The spatial Rokhlin property for actions of compact quantum groups. Journal of Functional Analysis, 272, pp. 2308-2360. (doi: 10.1016/j.jfa.2016.09.023)

Bartel, A., Lenstra, H. W. (2017) Commensurability of automorphism groups. Compositio Mathematica, 153, pp. 323-346. (doi: 10.1112/S0010437X1600823X)

Korff, C. (2017) Dimers, crystals and quantum Kostka numbers. Seminaire Lotharingien de Combinatoire, 78B.40, pp. 12pp.

Gadre, V. (2017) Partial sums of excursions along random geodesics and volume asymptotics for thin parts of moduli spaces of quadratic differentials. Journal of the European Mathematical Society, 19, pp. 3053-3089. (doi: 10.4171/JEMS/735)

Gadre, V., Maher, J., Tiozzo, G. (2017) Word length statistics for Teichmuller geodesics and singularity of harmonic measure. Commentarii Mathematici Helvetici, 92, pp. 1-36. (doi: 10.4171/CMH/404)

2016

Bartel, A., Page, A. (2016) Torsion homology and regulators of isospectral manifolds. Journal of Topology, 9, pp. 1237-1256. (doi: 10.1112/jtopol/jtw023)

Feigin, M. (2016) The Hilbert series of Λr,s(m). Appendix in Etingof, P., Rains, E. On Cohen–Macaulayness of algebras generated by generalized power sums. Communications in Mathematical Physics, 347, pp. 163-182. (doi: 10.1007/s00220-016-2657-0)

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)

Li, X. (2016) Semigroup C*-Algebras. (doi: 10.1007/978-3-319-39286-8_9)

Li, X. (2016) Semigroup C*-algebras of ax + b-semigroups. Transactions of the American Mathematical Society, 368, pp. 4417-4437. (doi: 10.1090/tran/6469)

Li, X. (2016) On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II. Advances in Mathematics, 291, pp. 1-11. (doi: 10.1016/j.aim.2015.12.024)

Korff, C. (2016) From quantum Bäcklund transforms to topological quantum field theory. Journal of Physics A: Mathematical and Theoretical, 49, (doi: 10.1088/1751-8113/49/10/104001)

Li, X., Norling, M. D. (2016) Independent resolutions for totally disconnected dynamical systems. II. C*-algebraic case. Journal of Operator Theory, 75, pp. 163-193. (doi: 10.7900/jot.2014dec22.2061)

Bartel, A., Dokchitser, T. (2016) Rational representations and permutation representations of finite groups. Mathematische Annalen, 364, pp. 539-558. (doi: 10.1007/s00208-015-1223-y)

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

Adler, V.E., Berest, Y. Y., Buchstaber, V.M., Grinevich, P.G., Dubrovin, B.A., Krichever, I.M., Novikov, S.P., Sergeev, A.N., Feigin, M.V., Felder, G., Ferapontov, E.V., Chalykh, O.A., Etingof, P.I. (2016) Alexander Petrovich Veselov (on his 60th birthday) Russian Mathematical Surveys, 71, pp. 1159-1176. (doi: 10.1070/RM9734)

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)

Gadre, V., Schleimer, S. (2016) The curves not carried. Groups, Geometry and Dynamics, 10, pp. 1249-1264. (doi: 10.4171/GGD/382)

Eilers, S., Li, X., Ruiz, E. (2016) The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids. Documenta Mathematica, 21, pp. 309-343.

2015

Feigin, M., Hakobyan, T. (2015) On Dunkl angular momenta algebra. Journal of High Energy Physics, 2015, (doi: 10.1007/JHEP11(2015)107)

Brendle, T. E., Margalit, D. (2015) Factoring in the hyperelliptic Torelli group. Mathematical Proceedings of the Cambridge Philosophical Society, 159, pp. 207-217. (doi: 10.1017/S0305004115000286)

Li, X. (2015) A new approach to recent constructions of C*-algebras from modular index theory. Journal of Functional Analysis, 269, pp. 841-864. (doi: 10.1016/j.jfa.2014.12.015)

Gadre, V., Maher, J., Tiozzo, G. (2015) Word length statistics and Lyapunov exponents for Fuchsian groups with cusps. New York Journal of Mathematics, 21, pp. 511-531.

Brown, K.A., O'Hagan, S., Zhang, J.J., Zhuang, G. (2015) Connected Hopf algebras and iterated Ore extensions. Journal of Pure and Applied Algebra, 219, pp. 2405-2443. (doi: 10.1016/j.jpaa.2014.09.007)

Brown, K., Gilmartin, P. (2015) Quantum homogeneous spaces of connected Hopf algebras. Journal of Algebra, 454, pp. 400-432.

Strachan, I., Brendle, T., Wilson, A. (2015) Online assessment and feedback: how to square the circle.

Brendle, T., Margalit, D., Putman, A. (2015) Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = -1. Inventiones Mathematicae, 200, pp. 263-310. (doi: 10.1007/s00222-014-0537-9)

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)

Li, X., Norling, M. D. (2015) Independent resolutions for totally disconnected dynamical systems I: algebraic case. Journal of Algebra, 424, pp. 98-125. (doi: 10.1016/j.jalgebra.2014.10.043)

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)

Bartel, A., Dokchitser, T. (2015) Brauer relations in finite groups. Journal of the European Mathematical Society, 17, pp. 2473-2512. (doi: 10.4171/JEMS/563)

Bhowmick, J., Voigt, C., Zacharias, J. (2015) Compact quantum metric spaces from quantum groups of rapid decay. Journal of Noncommutative Geometry, 9, pp. 1175-1200. (doi: 10.4171/JNCG/220)

Voigt, C., Yuncken, R. (2015) Equivariant Fredholm modules for the full quantum flag manifold of SUq(3) Documenta Mathematica, 20, pp. 433-490.

Cuntz, J., Echterhoff, S., Li, X. (2015) On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup. Journal of the European Mathematical Society, 17, pp. 645-687. (doi: 10.4171/JEMS/513)

Baker, A. (2015) Power operations and coactions in highly commutative homology theories. Publications of the Research Institute for Mathematical Sciences, 51, pp. 237-272. (doi: 10.4171/PRIMS/154)

Feigin, M. (2015) Propagation of sound waves. Mathematical Etudes. Institute of Mathematics of the Russian Academy of Sciences

Bartel, A. (2015) Simplicity of twists of abelian varieties. Acta Arithmetica, 171, pp. 15-22. (doi: 10.4064/aa171-1-2)

Brown, K. A., Goodearl, K. R. (2015) Zariski topologies on stratified spectra of quantum algebras. Cambridge University Press

Postgraduate research students

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Algebra - 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 Algebra and Number Theory 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.

The traditional objects of study in algebra are algebraic structures such as groups, rings, and modules. However, the developments of the last decades have increasingly emphasised the subject's connections with other areas of mathematics and science, such as number theory, geometry, topology, classical and quantum field theory, integrable systems, and theoretical computing science.

Here in Glasgow, we study both classical and modern problems and questions in algebra. The research interests of our staff members include geometric group theory, number theory (algebraic and analytic), both commutative and noncommutative ring theory, as well as topics in representation theory and homological algebra.  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.