Research & Events

Representation Theory of Algebras, Cluster Algebras, Algebraic Combinatorics, and Topological Data Analysis

Preprints & publications

1. "Brick infinite algebras admit infinitely many non-τ-rigid bricks", (arXiv:2606.27063).
   Coauthor: C. Paquette.
2. "Left modularity and extremality for (some) infinite lattices", (arXiv:2604.20947).
   Coauthors: S. Asai, O. Iyama, C. Paquette.
3. "Infinite string bricks and Sturmian words over some gentle algebras", (arXiv:2510.22377).
   Coauthors: M. Deaconu, C. Paquette.
4. "On the bricks (Schur representations) of finite dimensional algebras", (arXiv:2508.11789).
   Coauthor: C. Paquette.
5. "Brick-splitting torsion classes and Trim lattices", (arXiv:2506.13602).
   Coauthors: S. Asai, O. Iyama, C. Paquette.
6. "Geometric interactions between bricks and τ-rigidity", (arXiv:2311.14863).
   Coauthor: C. Paquette.
7. "A Continuous Associahedron of Type A", (arXiv & Journal), Mathematische Zeitschrift (2026).
   Coauthors: M. Kulkarni, J. Matherne, J. Rock.
8. "Hom-Orthogonal modules and brick-Brauer-Thrall conjectures", (arXiv & Journal), Journal of Algebra (2025).
   Coauthor: C. Paquette.
9. "Biserial algebras and generic bricks", (arXiv & Journal), Mathematische Zeitschrift (2025).
   Coauthor: C. Paquette.
10. "ABHY associahedra and Newton polytopes of F-polynomials for cluster algebras of simply laced finite type", (arXiv & Journal), Journal of the London Mathematical Society (2024).
    Coauthors: V. Bazier-Matte, N. Chapelier-Laget, G. Douville, H. Thomas, E. Yıldırım.
11. "Minimal (τ-)tilting infinite algebras", (arXiv & Journal), Nagoya Mathematical Journal (2023).
    Coauthor: C. Paquette.
12. "τ-Tilting finiteness of biserial algebras", (arXiv & Journal), Algebras and Representation Theory (2023).
13. "τ-Tilting finiteness of non-distributive algebras and their module varieties", (arXiv & Journal), Journal of Algebra (2022).
14. "On the combinatorics of gentle algebras", (arXiv & Journal), Canadian Journal of Mathematics (2020).
    Coauthors: T. Brüstle, G. Douville, H. Thomas, E. Yıldırım.
15. "A categorification of biclosed sets of strings", (arXiv & Journal), Journal of Algebra (2020).
    Coauthors: A. Garver, T. McConville.
16. "On Some Properties of Toeplitz Matrices", (Journal), Cogent Mathematics (2016).
    Coauthors: D. Kucerovsky, A. Sarraf.

Other writings

• PhD Dissertation: "τ-tilting finiteness of minimal representation-infinite algebras" (Defended June 2020).
• Extended Abstract: "Distribution of bricks and an open algebro-geometric conjecture" (Unpublished).
• Research Note: "Strict Dihedral Algebras are tau-tilting finite" (Not for publication, yet!).
• Extended Abstract: "Left modularity and extremality through brick-directed algebras" (To appear, Proceedings of FPSAC 38, Seattle, 2026).

Posters

• Left modular and Extremal lattices through brick-directed algebras
• Locally representation-directed algebras, realized & generalized via generically τ-reduced components
• Generic brick-Brauer-Thrall Conjecture
• Towards a classification of Minimal (τ-)Tilting Infinite Algebras
• τ-Tilting theory of Gentle Algebras

Academic events (co-)organization

Upcoming

• J-PEAKS Workshop on Interface of Multiparameter Persistence and Representation Theory Interleaved with New Topics (IMPRINT) Okinawa, Japan · February 1–5, 2027 · Website currently unavailable to the public
• CIRM Research School on Geometric Representation theory in multipArameter PErsistence (GRAPE) Luminy, France · June 7–11, 2027 · conferences.cirm-math.fr

Past

• Workshop on Spectrums in Representation Theory of Algebras and Related TopicsOCAMI, Japan · December 16–19, 2025 · website
• Thematic Program: TDA PARTI — Topological Data Analysis, Persistence And Representation Theory IntertwinedOIST, Japan · June 23–August 9, 2025 · website
• Workshop on Bricks and Endofinite RepresentationsBielefeld, Germany · March 3–5, 2025 · website
• Winter School on Large Modules and EndofinitenessStuttgart, Germany · February 24–28, 2025 · website
• Autumn School & Conference on New Developments in Representation Theory of AlgebrasOkinawa, Japan · November 18–30, 2024 · website
• Summer Research School on Applications of Representation Theory in Topological Data Analysis and Geometric Invariant TheoryMontreal, Canada · June 3–7, 2024 · website
• Spring Workshop on the Representation Theory of Algebras and related areasOkinawa, Japan · April 22–26, 2024 · website
• Advances in Representation Theory of Algebras (ARTA IX)Kingston, Canada · June 12–16, 2023 · website
• Representation Theory of Algebras — Special Session, Canadian Mathematical Society Winter Meeting 2022Toronto, Canada · December 2–5, 2022 · website
• Mutations: From Cluster Algebras to Representation Theory — ISM Discovery research schoolMontreal, Canada · July 4–8, 2022 · website
• Representation Theory and Geometry — online conference during the Covid periodHosted by Queen's University, Canada · February 14–16, 2022 · website