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Categories, Clusters and Completions

Publications

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Gratz, S. & Stevenson, G. (2023). Approximating triangulated categories by spaces. Elsevier. https://doi.org/10.1016/j.aim.2023.109073

August, J., Cheung, M. W., Faber, E., Gratz, S. & Schroll, S. (2023). Cluster structures for the A_∞ singularity. Journal of the London Mathematical Society, 107(6), 2121-2149. https://doi.org/10.1112/jlms.12735

Gratz, S. & Zvonareva, A. (2023). Lattices of t-structures and thick subcategories for discrete cluster categories. Journal of the London Mathematical Society, 107(3), 973-1001. https://doi.org/10.1112/jlms.12705

August, J., Cheung, M. W., Faber, E., Gratz, S. & Schroll, S. (2024). Categories for Grassmannian Cluster Algebras of Infinite Rank. International Mathematics Research Notices, 2024(2), 1166-1210. https://doi.org/10.1093/imrn/rnad004

Gratz, S., Raedschelders, T., Špenko, Š. & Stevenson, G. (2024). Homotopy Invariants for gradable finite dimensional algebras.

Cummings, C. (2024). Left-right symmetry of finite finitistic dimension. Bulletin of the London Mathematical Society, 56(2), 624-633. https://doi.org/10.1112/blms.12954

Cummings, C. & Gratz, S. (2024). Metric completions of discrete cluster categories.

Gratz, S., Holm, H., Jorgensen, P. & Stevenson, G. (2024). Tilting in $Q$-shaped derived categories.

Grabowski, J. E. & Gratz, S. (2025). Abstract Cluster Structures.

Cummings, C., Gratz, S., Kirkman, E., Letz, J. C., Rock, J. D. & Špenko, Š. (2025). An equivalence linking CM-types $A_\infty$ and $D_\infty$.

Gratz, S. & Korff, C. (2025). Ind-cluster algebras and infinite Grassmannians.

Matousek, C. (2026). Metric completions of triangulated categories from finite dimensional algebras. Advance online publication. https://doi.org/10.48550/arXiv.2409.01828

Matousek, C. (2026). Metric completions of triangulated categories from hereditary rings. https://doi.org/10.48550/arXiv.2508.20283

Revised 20.03.2026

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Lars Madsen