Geometry & topology

Our research interests include algebraic topology, geometric group theory, dynamics, and manifold topology, especially manifolds of dimension two, three and four.




Feigin, M., Valeri, D., Wright, J. (2024) Flat coordinates of algebraic Frobenius manifolds in small dimensions. Journal of Geometry and Physics, 200, (doi: 10.1016/j.geomphys.2024.105151)

Friedl, S., Nagel, M., Orson, P., Powell, M. (2024) The foundations of four-manifold theory in the topological category. New York Journal of Mathematics,

Brownlowe, N., Buss, A., Goncalves, D., Hume, J. B., Sims, A., Whittaker, M. F. (2024) KK-duality for self-similar groupoid actions on graphs. Transactions of the American Mathematical Society,

Gadre, V., Hensel, S. (2024) Linear progress in fibres. Groups, Geometry and Dynamics, (doi: 10.4171/GGD/780)

Boyd, R., Hepworth, R., Patzt, P. (2024) The homology of the partition algebras. Pacific Journal of Mathematics, 327, pp. 1-27. (doi: 10.2140/pjm.2023.327.1)

Orson, P., Powell, M. (2024) Simple spines of homotopy 2-spheres are unique. Proceedings of the London Mathematical Society, 128, (doi: 10.1112/plms.12583)

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

Boyd, R., Charney, R., Morris-Wright, R., Rees, S. (2024) The Artin monoid Cayley graph. Journal of Combinatorial Algebra, (doi: 10.4171/JCA/85)


Brejevs, V., Wand, A. (2023) Stein-fillable open books of genus one that do not admit positive factorisations. Mathematical Research Letters, 30, pp. 709-719. (doi: 10.4310/MRL.2023.v30.n3.a4)

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)

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)

Conway, A., Crowley, D., Powell, M. (2023) Infinite homotopy stable class for 4-manifolds with boundary. Pacific Journal of Mathematics, 325, pp. 209-237. (doi: 10.2140/pjm.2023.325.209)

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)

Hayden, K., Kjuchukova, A., Krishna, S., Miller, M., Powell, M., Sunukjian, N. (2023) Brunnian exotic surface links in the 4-ball. Michigan Mathematical Journal,

Kutluhan, C., Matic, G., Van Horn Morris, J., Wand, A. (2023) Filtering the Heegaard Floer contact invariant. Geometry and Topology, 27, pp. 2181-2236. (doi: 10.2140/gt.2023.27.2181)

Greene, J. E., Owens, B. (2023) Alternating links, rational balls, and cube tilings. Journal of the European Mathematical Society,

Kasprowski, D., Powell, M., Teichner, P. (2023) Algebraic criteria for stable diffeomorphism of spin 4-manifolds. Memoirs of the American Mathematical Society,

Miller, A. N., Powell, M. (2023) Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group. Journal of the London Mathematical Society, 107, pp. 2025-2053. (doi: 10.1112/jlms.12732)

Conway, A., Powell, M. (2023) Embedded surfaces with infinite cyclic knot group. Geometry and Topology, 27, pp. 739-821. (doi: 10.2140/gt.2023.27.739)

Azemar, A. (2023) A qualitative description of the horoboundary of the Teichmüller metric. Algebraic and Geometric Topology,

Belk, J., Matucci, F. (2023) Conjugator length in Thompson’s groups. Bulletin of the London Mathematical Society, 55, pp. 793-810. (doi: 10.1112/blms.12757)

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)

Kasprowski, D., Powell, M., Ray, A., Teichner, P. (2023) Embedding surfaces in 4-manifolds. Geometry and Topology,

Kasprowski, D., Powell, M., Ray, A. (2023) Gluck twists on concordant or homotopic spheres. Mathematical Research Letters,

Owens, B., Swenton, F. (2023) An algorithm to find ribbon disks for alternating knots. Experimental Mathematics, (doi: 10.1080/10586458.2022.2158968)

Kasprowski, D., Powell, M., Ray, A. (2023) Counterexamples in 4-manifold topology. EMS Surveys in Mathematical Sciences, 9, pp. 193-249. (doi: 10.4171/EMSS/56)

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

Feller, P., Park, J., Powell, M. (2023) The Z-genus of boundary links. Revista Matemática Complutense, 36, pp. 1-25. (doi: 10.1007/s13163-022-00424-3)

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

Belk, J., Elliott, L., Matucci, F. (2023) A short proof of Rubin’s theorem. Israel Journal of Mathematics,

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)

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

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


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)

Orson, P., Powell, M. (2022) Doubly slice knots and metabelian obstructions. Journal of Topology and Analysis, 14, pp. 847-873. (doi: 10.1142/S1793525321500229)

Belk, J., Lanier, J., Margalit, D., Winarski, R. R. (2022) Recognizing topological polynomials by lifting trees. Duke Mathematical Journal, 171, pp. 3401-3480. (doi: 10.1215/00127094-2022-0043)

Owens, B., Strle, S. (2022) Disoriented homology and double branched covers. Canadian Journal of Mathematics, (doi: 10.4153/S0008414X22000591)

Azemar, A. (2022) Random walks on convergence groups. Groups, Geometry and Dynamics, 16, pp. 581-612. (doi: 10.4171/ggd/654)

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)

Park, J., Powell, M. (2022) A ribbon obstruction and derivatives of knots. Israel Journal of Mathematics, 250, pp. 265-305. (doi: 10.1007/s11856-022-2338-y)

Conway, A., Crowley, D., Powell, M., Sixt, J. (2022) Simply connected manifolds with large homotopy stable classes. Journal of the Australian Mathematical Society, (doi: 10.1017/S1446788722000167)

Bédaride, N., Gähler, F., Lecuona, A. G. (2022) Cohomology Groups for Spaces of Twelve-Fold Tilings. International Mathematics Research Notices, 2022, pp. 14181-14254. (doi: 10.1093/imrn/rnab117)

Friedl, S., Kitayama, T., Lewark, L., Nagel, M., Powell, M. (2022) Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials. Canadian Journal of Mathematics, 74, pp. 1137-1176. (doi: 10.4153/S0008414X21000183)

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

Wilson, A. (2022) Maths Inside Photo Exhibition 2022, Kibble Palace, Glasgow Botanical Gardens.

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)

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)

Kasprowski, D., Powell, M., Teichner, P. (2022) Four-manifolds up to connected sum with complex projective planes. American Journal of Mathematics, 144, pp. 75-118. (doi: 10.1353/ajm.2022.0001)

Belk, J., Hyde, J., Matucci, F. (2022) Embedding Q into a finitely presented group. Bulletin of the American Mathematical Society, 59, pp. 561-567. (doi: 10.1090/bull/1762)

Degtyarev, A., Florens, V., Lecuona, A. G. (2022) Slopes and signatures of links. Fundamenta Mathematicae, 258, pp. 65-114. (doi: 10.4064/fm136-1-2022)

Belk, J., Zaremsky, M. C. B. (2022) Twisted Brin-Thompson groups. Geometry and Topology, 26, pp. 1189-1223. (doi: 10.2140/gt.2022.26.1189)


Owens, B. (2021) Knots and 4-manifolds. Winter Braids Lecture Notes, 6, (doi: 10.5802/wbln.28)

Conway, A., Powell, M. (2021) Characterisation of homotopy ribbon discs. Advances in Mathematics, 391, (doi: 10.1016/j.aim.2021.107960)

Walton, J. J., Whittaker, M. F. (2021) An aperiodic tile with edge-to-edge orientational matching rules. Journal of the Institute of Mathematics of Jussieu, (doi: 10.1017/S1474748021000517)

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)

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)

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)

(2021) The Disc Embedding Theorem.

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

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

Orson, P., Powell, M. (2021) A lower bound for the doubly slice genus from signatures. New York Journal of Mathematics, 27, pp. 379-392.

Stedman, R., Strachan, I. A.B. (2021) Extended ⋁-systems and trigonometric solutions to the WDVV equations. Journal of Mathematical Physics, 62, (doi: 10.1063/5.0024108)

Kasprowski, D., Lambert-Cole, P., Land, M., Lecuona, A. G. (2021) Topologically flat embedded 2-spheres in specific simply connected 4-manifolds. Springer

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

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)

Strachan, I. A.B., Bridgeland, T. (2021) Complex hyperkähler structures defined by Donaldson–Thomas invariants. Letters in Mathematical Physics, 111, (doi: 10.1007/s11005-021-01388-z)

Feller, P., Miller, A. N., Nagel, M., Orson, P., Powell, M., Ray, A. (2021) Embedding spheres in knot traces. Compositio Mathematica, 157, pp. 2242-2279. (doi: 10.1112/s0010437x21007508)

Belk, J., Bleak, C., Matucci, F. (2021) Rational embeddings of hyperbolic groups. Journal of Combinatorial Algebra, 5, pp. 123-183. (doi: 10.4171/JCA/52)

Kim, M. H., Powell, M., Teichner, P. (2021) Round handle problem. Pure and Applied Mathematics Quarterly, 17, pp. 237-347. (doi: 10.4310/PAMQ.2021.v17.n1.a6)

Degtyarev, A., Florens, V., Lecuona, A. G. (2021) Slopes of links and signature formulas. American Mathematical Society

Cha, J. C., Miller, A. N., Powell, M. (2021) Two-solvable and two-bipolar knots with large four-genera. Mathematical Research Letters, 28, pp. 331-382. (doi: 10.4310/MRL.2021.v28.n2.a2)


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)

Friedl, S., Powell, M. (2020) Homotopy ribbon concordance and Alexander polynomials. Archiv der Mathematik, 115, pp. 717-725. (doi: 10.1007/s00013-020-01517-5)

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)

Mampusti, M., Whittaker, M. F. (2020) An aperiodic monotile that forces nonperiodicity through dendrites. Bulletin of the London Mathematical Society, 52, pp. 942-959. (doi: 10.1112/blms.12375)

Easo, P., Garijo, E., Kaubrys, S., Nkansah, D., Vrabec, M., Watt, D., Wilson, C., Bönicke, C., Evington, S., Forough, M., Girón Pacheco, S., Seaton, N., White, S., Whittaker, M. F., Zacharias, J. (2020) The Cuntz-Toeplitz algebras have nuclear dimension one. Journal of Functional Analysis, 279, (doi: 10.1016/j.jfa.2020.108690)

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

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

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)

Owens, B. (2020) Smooth, nonsymplectic embeddings of rational balls in the complex projective plane. Quarterly Journal of Mathematics, 71, pp. 997-1007. (doi: 10.1093/qmathj/haaa013)

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)

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

Baird, N., Shah, T. B., Clacy, A., Gerontogiannis, D., Mackenzie, J., Nkansah, D., Quinn, J., Spencer-Wood, H., Thomson, K., Wilson, A. (2020) maths inside Resource Suite with Interdisciplinary Learning Activities. (doi: 10.36399/gla.pubs.234071)

Cha, J. C., Kim, M. H., Powell, M. (2020) A family of freely slice good boundary links. Mathematische Annalen, 376, pp. 1009-1030. (doi: 10.1007/s00208-019-01907-3)

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)

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

Cha, J. C., Orr, K. E., Powell, M. (2020) Whitney towers and abelian invariants of knots. Mathematische Zeitschrift, 294, pp. 519-553. (doi: 10.1007/s00209-019-02293-x)

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

Davis, C. W., Nagel, M., Orson, P., Powell, M. (2020) Surface systems and triple linking numbers. Indiana University Mathematics Journal, 69, pp. 2505-2547. (doi: 10.1512/iumj.2020.69.8081)

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)


Nagel, M., Orson, P., Park, J., Powell, M. (2019) Smooth and topological almost concordance. International Mathematics Research Notices, 2019, pp. 7324-7355. (doi: 10.1093/imrn/rnx338)

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)

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

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

Lecuona, A. G. (2019) Complementary legs and rational balls. Michigan Mathematical Journal, 68, pp. 637-649. (doi: 10.1307/mmj/1561708817)

Dubrovin, B., Strachan, I. A.B., Zhang, Y., Zuo, D. (2019) Extended affine Weyl groups of BCD-type: their Frobenius manifolds and their Landau-Ginzburg superpotentials. Advances in Mathematics, 351, pp. 897-946. (doi: 10.1016/j.aim.2019.05.030)

Wilson, A., McEwan, M. (2019) Playfulness in Higher Education.

Wilson, A., McEwan, M. (2019) Embedding Play in Mathematics: Building an Evidence Base.

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

Wilson, A., McEwan, M. (2019) Embedding Play in Higher Education: Building an Evidence Base.

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

Friedl, S., Nagel, M., Orson, P., Powell, M. (2019) Satellites and concordance of knots in 3–manifolds. Transactions of the American Mathematical Society, 371, pp. 2279-2306. (doi: 10.1090/tran/7313)

Kutluhan, C., Matic, G., Van Horn-Morris, J., Wand, A. (2019) A Heegaard Floer analog of algebraic torsion. (doi: 10.1090/pspum/102)

Strachan, I. A.B. (2019) A construction of multidimensional Dubrovin-Novikov brackets. Journal of Nonlinear Mathematical Physics, 26, pp. 202-213. (doi: 10.1080/14029251.2019.1591716)

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)

Miller, A. N., Powell, M. (2019) Stabilization distance between surfaces. L’Enseignement Mathématique, 65, pp. 397-440. (doi: 10.4171/lem/65-3/4-4)


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

Deeley, R., Goffeng, M., Mesland, B., Whittaker, M. F. (2018) Wieler solenoids, Cuntz-Pimsner algebras and K-theory. Ergodic Theory and Dynamical Systems, 38, pp. 2942-2988. (doi: 10.1017/etds.2017.10)

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

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)

Owens, B. (2018) Equivariant embeddings of rational homology balls. Quarterly Journal of Mathematics, 69, pp. 1101-1121. (doi: 10.1093/qmath/hay016)

Aceto, P., Golla, M., Lecuona, A. G. (2018) Handle decompositions of rational homology balls and Casson–Gordon invariants. Proceedings of the American Mathematical Society, 146, pp. 4059-4072. (doi: 10.1090/proc/14035)

Wilson, A. (2018) *maths inside* Maths Week Scotland 2018 Photograph Competition.

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)

Lecuona, A. G. (2018) A note on graphs and rational balls. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 112, pp. 705-716. (doi: 10.1007/s13398-017-0464-x)

Laca, M., Raeburn, I., Ramagge, J., Whittaker, M. F. (2018) Equilibrium states on operator algebras associated to self-similar actions of groupoids on graphs. Advances in Mathematics, 331, pp. 268-325. (doi: 10.1016/j.aim.2018.03.030)

Audoux, B., Lecuona, A. G., Roukema, F. (2018) On hyperbolic knots in S³ with exceptional surgeries at maximal distance. Algebraic and Geometric Topology, 18, pp. 2371-2417. (doi: 10.2140/agt.2018.18.2371)

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)

Wilson, A.J. (2018) Embedding Play in Higher Education.

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

Miller, A. N., Powell, M. (2018) Symmetric chain complexes, twisted Blanchfield pairings and knot concordance. Algebraic and Geometric Topology, 18, pp. 3425-2476. (doi: 10.2140/agt.2018.18.3425)

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)


Nagel, M., Powell, M. (2017) Concordance invariance of Levine-Tristram signatures of links. Documenta Mathematica, 22, pp. 25-43. (doi: 10.25537/dm.2017v22.25-43)

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)

Powell, M., Cochran, T. D., Harvey, S. (2017) Grope metrics on the knot concordance set. Journal of Topology, 10, pp. 669-699. (doi: 10.1112/topo.12018)

Kaminker, J., Putnam, I. F., Whittaker, M. F. (2017) K-theoretic duality for hyperbolic dynamical systems. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 2017, pp. 263-299. (doi: 10.1515/crelle-2014-0126)

Kasprowski, D., Land, M., Powell, M., Teichner, P. (2017) Stable classification of 4-manifolds with 3-manifold fundamental groups. Journal of Topology, 10, pp. 827-881. (doi: 10.1112/topo.12025)

Cha, J. C., Friedl, S., Powell, M. (2017) Splitting numbers of links. Proceedings of the Edinburgh Mathematical Society, 60, pp. 587-614. (doi: 10.1017/S0013091516000420)

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

Strachan, I. A.B., Zuo, D. (2017) Frobenius manifolds and Frobenius algebra-valued integrable systems. Letters in Mathematical Physics, 107, pp. 997-1026. (doi: 10.1007/s11005-017-0939-x)

Brownlowe, N., Pask, D., Ramagge, J., Robertson, D., Whittaker, M. (2017) Zappa-Szép product groupoids and C*-blends. Semigroup Forum, 94, pp. 500-519. (doi: 10.1007/s00233-016-9775-z)

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)

Brownlowe, N., Carlsen, T. M., Whittaker, M. (2017) Graph algebras and orbit equivalence. Ergodic Theory and Dynamical Systems, 37, pp. 389-417. (doi: 10.1017/etds.2015.52)

Degtyarev, A., Florens, V., Lecuona, A. G. (2017) The signature of a splice. International Mathematics Research Notices, 2017, pp. 2249-2283. (doi: 10.1093/imrn/rnw068)

Strachan, I. A.B., Stedman, R. (2017) Generalized Legendre transformations and symmetries of the WDVV equations. Journal of Physics A: Mathematical and Theoretical, 50, (doi: 10.1088/1751-8121/aa58b2)

Mampusti, M., Whittaker, M. F. (2017) Fractal spectral triples on Kellendonk's C*-algebra of a substitution tiling. Journal of Geometry and Physics, 112, pp. 224-239. (doi: 10.1016/j.geomphys.2016.11.010)

Powell, M. (2017) The four-genus of a link, Levine–Tristram signatures and satellites. Journal of Knot Theory and Its Ramifications, 26, (doi: 10.1142/s0218216517400089)

Friedl, S., Powell, M. (2017) A calculation of Blanchfield pairings of 3-manifolds and knots. Moscow Mathematical Journal, 17, pp. 59-77. (doi: 10.17323/1609-4514-2017-17-1-59-77)

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)

Fruedk, S., Leidy, C., Nagel, M., Powell, M. (2017) Twisted Blanchfield pairings and decompositions of 3-manifolds. Homology, Homotopy and Applications, 19, pp. 275-287. (doi: 10.4310/HHA.2017.v19.n2.a14)

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)


Powell, M. (2016) Twisted Blanchfield pairings and symmetric chain complexes. Quarterly Journal of Mathematics, 67, pp. 715-742. (doi: 10.1093/qmath/haw028)

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)

Deeley, R., Killough, D. B., Whittaker, M. (2016) Dynamical correspondences for Smale spaces. New York Journal of Mathematics, 22, pp. 943-988.

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)

Cha, J. C., Powell, M. (2016) Casson towers and slice links. Inventiones Mathematicae, 205, pp. 413-457. (doi: 10.1007/s00222-015-0639-z)

Deeley, R. J., Killough, D. B., Whittaker, M. F. (2016) Functorial properties of Putnam's homology theory for Smale spaces. Ergodic Theory and Dynamical Systems, 36, pp. 1411-1440. (doi: 10.1017/etds.2014.134)

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)

Borodzik, M., Friedl, S., Powell, M. (2016) Blanchfield forms and Gordian distance. Journal of the Mathematical Society of Japan, 68, pp. 1047-1080. (doi: 10.2969/jmsj/06831047)

Borodzik, M., Powell, M. (2016) Embedded Morse theory and relative splitting of cobordisms of manifolds. Journal of Geometric Analysis, 26, pp. 57-87. (doi: 10.1007/s12220-014-9538-6)

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)

Frank, N. P., Webster, S. B.G., Whittaker, M. (2016) Fractal dual substitution tilings. Journal of Fractal Geometry, 3, pp. 265-317. (doi: 10.4171/JFG/37)

Owens, B., Strle, S. (2016) Immersed disks, slicing numbers and concordance unknotting numbers. Communications in Analysis and Geometry, 24, pp. 1107-1138. (doi: 10.4310/CAG.2016.v24.n5.a8)

Baker, K. L., Buck, D., Lecuona, A. G. (2016) Some knots in S¹ x S² with lens space surgeries. Communications in Analysis and Geometry, 24, pp. 431-470. (doi: 10.4310/CAG.2016.v24.n3.a1)

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

Kumjian, A., Pask, D., Sims, A., Whittaker, M. F. (2016) Topological spaces associated to higher-rank graphs. Journal of Combinatorial Theory, Series A, 143, pp. 19-41. (doi: 10.1016/j.jcta.2016.04.005)

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)


Wand, A. (2015) Detecting tightness via open book decompositions. Geometry and Topology Monographs, 19, pp. 291-317. (doi: 10.2140/gtm.2015.19.291)

Nagel, M., Owens, B. (2015) Unlinking information from 4-manifolds. Bulletin of the London Mathematical Society, 47, pp. 964-979. (doi: 10.1112/blms/bdv072)

Strachan, I. A.B., Zuo, D. (2015) Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy. Journal of Mathematical Physics, 56, (doi: 10.1063/1.4935936)

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

Wand, A. (2015) Factorizations of diffeomorphisms of compact surfaces with boundary. Geometry and Topology, 19, pp. 2407-2464. (doi: 10.2140/gt.2015.19.2407)

Lecuona, A. G. (2015) On the slice-ribbon conjecture for pretzel knots. Algebraic and Geometric Topology, 15, pp. 2133-2173. (doi: 10.2140/agt.2015.15.2133)

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)

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.

Wand, A. (2015) Surgery and Tightness in Contact 3-Manifolds.

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)

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

Lisca, P., Owens, B. (2015) Signatures, Heegaard Floer correction terms and quasi-alternating links. Proceedings of the American Mathematical Society, 143, pp. 907-915. (doi: 10.1090/S0002-9939-2014-12265-9)

Wand, A. (2015) Tightness is preserved by Legendrian surgery. Annals of Mathematics, 182, pp. 723-738. (doi: 10.4007/annals.2015.182.2.8)

Postgraduate research students

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Geometry and Topology - 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.


Regular seminars relevant to the group are held as part of the Geometry and Topology 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.


Geometry and Topology at the University of Glasgow touches on a wide range of highly active subdisciplines, benefiting from and capitalizing on strong overlap with the Algebra, Analysis, and Integrable Systems and Mathematical Physics research groups within the School of Mathematics and Statistics.

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

Our interests lie in algebraic topology, geometric group theory, low-dimensional topology and quantum geometry, to name a few.

Broadly speaking, our research – performed by undergraduates, postgraduates, postdoctoral fellows, and academic staff – is concerned with the rich interaction and deep interconnections between algebra and geometry with a view to new applications and solutions to long-standing problems.