A Lagrangian filling for every cluster seed
R Casals, H Gao - Inventiones mathematicae, 2024 - Springer
We show that each cluster seed in the augmentation variety contains an embedded exact
Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian fillings …
Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian fillings …
[HTML][HTML] Mutation of frozen Jacobian algebras
M Pressland - Journal of Algebra, 2020 - Elsevier
We survey results on mutations of Jacobian algebras, while simultaneously extending them
to the more general setup of frozen Jacobian algebras, which arise naturally from dimer …
to the more general setup of frozen Jacobian algebras, which arise naturally from dimer …
Riemann-Hilbert problems from rank 3 WKB spectral networks
D Wu - arXiv preprint arXiv:2311.03922, 2023 - arxiv.org
We extract cluster structures and establish spectral coordinates from rank 3 WKB spectral
networks $\mathcal W (\varphi,\vartheta) $ when zeros of $\varphi (z) $ are almost on a line …
networks $\mathcal W (\varphi,\vartheta) $ when zeros of $\varphi (z) $ are almost on a line …
A correspondence between additive and monoidal categorifications with application to Grassmannian cluster categories
K Baur, C Fu, J Li - arXiv preprint arXiv:2410.04401, 2024 - arxiv.org
Building on work of Derksen-Fei and Plamondon, we formulate a conjectural
correspondence between additive and monoidal categorifications of cluster algebras, which …
correspondence between additive and monoidal categorifications of cluster algebras, which …
Finite dimensional 2-cyclic Jacobian algebras
Y Li, L Peng - arXiv preprint arXiv:2408.10056, 2024 - arxiv.org
In this paper, we start with a class of quivers containing only 2-cycles and loops, referred to
as 2-cyclic quivers. We prove that there exists a potential on these quivers that ensures the …
as 2-cyclic quivers. We prove that there exists a potential on these quivers that ensures the …