Papers
Preprints
| 15. | Cluster structures via representation theory: cluster ensembles, tropical duality, cluster characters and quantisation, with Jan E. Grabowski. Preprint available on arXiv. |
| 14. | Reduction of Frobenius extriangulated categories, with Eleonore Faber and Bethany Marsh. Preprint available on arXiv. |
| 13. | Extriangulated ideal quotients, with applications to cluster theory and gentle algebras, with Xin Fang, Mikhail Gorsky, Yann Palu and Pierre-Guy Plamondon. Preprint available on arXiv. |
| 12. | Quasi-coincidence of cluster structures on positroid varieties. Preprint available on arXiv. |
Publications
| 11. | Cluster categories for completed infinity-gons I: Categorifying triangulations, J. Lond. Math. Soc. 111 (2025), Paper No. e70092, with İlke Çanakçı and Martin Kalck. Journal version available online (open access), final version available on arXiv. |
| 10. | Perfect matching modules, dimer partition functions and cluster characters, Adv. Math 443 (2024), Paper No. 109570, with İlke Çanakçı and Alastair King. Journal version available online (open access), final version available on arXiv. |
| 9. | From frieze patterns to cluster categories, in Modern Trends in Algebra and Representation Theory, London Math. Soc. Lecture Note Ser. Vol. 486, CUP (2023), 109–145. Published version available online (with subscription), final version available on arXiv. |
| 8. | A categorification of acyclic principal coefficient cluster algebras, Nagoya Math. J. 252 (2023), 769–809. Journal version available online (open access), final version available on arXiv. |
| 7. | Calabi–Yau properties of Postnikov diagrams, Forum Math. Sigma 10 (2022), Paper No. e56. Journal version available online (open access), final version available on arXiv. |
| 6. |
On quiver Grassmannians and orbit closures for gen‐finite modules, Algebr. Represent. Theory 25 (2022), no. 2, 413–445, with Julia Sauter.
Journal version available online (open access), accepted manuscript available on arXiv. Summary (with same title) available in Proceedings of the 50th Symposium on Ring Theory and Representation Theory (2018), 155–164. |
| 5. | Special tilting modules for algebras with positive dominant dimension, Glasg. Math. J. 64 (2022), no. 1, 79–105, with Julia Sauter. Journal version available online (open access), accepted manuscript available on arXiv. |
| 4. | Mutation of frozen Jacobian algebras, J. Algebra 546 (2020), 236–273. Corrigendum, J. Algebra 588 (2021), 533–537. Journal version and corrigendum available online (with subscription), accepted manuscript including corrigendum available on arXiv. The corrigendum gives various corrected versions of Proposition 5.16 from the original (which was false as stated), and addresses some other more minor inaccuracies. |
| 3. | Graded Frobenius cluster categories, Doc. Math. 23 (2018), 49–76, with Jan E. Grabowski. Journal version available online (open access), final version available on arXiv. |
| 2. | Internally Calabi–Yau algebras and cluster‐tilting objects, Math. Z. 287 (2017), no. 1–2, 555–585. Journal version available online (open access), final version available on arXiv. |
| 1. | Labelled seeds and the mutation group, Math. Proc. Cambridge Philos. Soc. 163 (2017), no. 2, 193–217, with Alastair King. Journal version available online (with subscription), accepted manuscript available on arXiv. |
Other
| Positroid varieties and quasi-coincidence via representation theory. Oberwolfach Report for Cluster Algebras and Its Applications (2024). |
| Double Bruhat cells and generalisations. Oberwolfach Report for Arbeitsgemeinschaft: Cluster Algebras (2023). Correction: I completely misunderstood some notation when writing the final section on double Bott–Samelson varieties: for constructing the quiver, one in fact follows an identical procedure to that for double Bruhat cells, still using the Dynkin diagram \(\Delta\) (but now allowing arbitrary positive braids in place of Weyl group elements). Only if the generalised Cartan matrix \(C\) is non-invertible, so the Lie group is not semi-simple, is it necessary to add additional open strings, of number equal to the corank of \(C\). | Auslander–Reiten translations for Gorenstein algebras, with Sondre Kvamme. Appendix to ‘Monomial Gorenstein algebras and the stably Calabi–Yau property’, Algebr. Represent. Theory 24 (2021), 1083–1099, by Ana García Elsener. Journal version available online (open access), submitted version available on arXiv. Correction: The functor \(\Sigma\) is defined via left (not right) \(\operatorname{proj}\Lambda\)‐approximation. |
| Frobenius categorification of cluster algebras. Ph.D. thesis, available on Bath Research Portal (open access) and EThOS (requires registration). |