Research Interests
My research is in cluster algebras and more generally in representation theory. I currently focus on obtaining a deeper understanding of scattering diagrams (also known as wall-crossing structures) from both combinatorial and representation-theoretic perspectives, and on advancing the categorification of cluster algebras associated with skew-symmetrizable exchange matrices.
Preprints and Publications
Mutations of quivers with 2-cycles, with Fang Li, Siyang Liu, Jie Pan.
Positivity of generalized cluster scattering diagrams, with Amanda Burcroff and Kyungyong Lee.
Scattering diagrams, tight gradings, and generalized positivity, with Amanda Burcroff and Kyungyong Lee.
Proc. Natl. Acad. Sci. USA. 122, 18, e2422893122, (2025). arXiv:2409.15235
Generic bases of skew-symmetrizable affine type cluster algebras, with Xiuping Su.
Gentle algebras arising from surfaces with orbifold points, Part II: Locally free Caldero–Chapoton functions, with Daniel Labardini-Fragoso.
Locally free Caldero–Chapoton functions via reflections.
Math. Z. 307, 11 (2024). arXiv:2206.02289
Gentle algebras arising from surfaces with orbifold points of order 3, Part I: scattering diagrams, with Daniel Labardini-Fragoso.
Algebr. Represent. Theory 27, 679–722 (2024). arXiv:2203.11563
Scattering diagrams for generalized cluster algebras.
Algebra Number Theory 18, 2179–2246 (2024). arXiv:2110.02416
Wall-crossing structures in cluster algebras, Ph.D. Thesis (2020), available here.
Scattering diagrams of quivers with potentials and mutations.
Notes
Stability measures on triangulated categories, with Eric Babson.
Contact
langmou at math dot uni-koeln dot de
lmou dot math at gmail dot com