36 citations · 99 across the 16 of their papers we have counts for
18 papers
Valuative independence and cluster theta reciprocity
Man-Wai Cheung, Timothy Magee, Travis Mandel +1
We prove that theta functions constructed from positive scattering diagrams satisfy valuative independence. That is, for certain valuations , we have $\oper…
Newton--Okounkov bodies and minimal models for cluster varieties
Lara Bossinger, Man-Wai Cheung, Timothy Magee +1
Let be a (partial) minimal model of a scheme with a cluster structure. Under natural assumptions, for every choice of seed we associate a Newton--Okounkov body to every div…
Clustering Cluster Algebras with Clusters
Man-Wai Cheung, Pierre-Philippe Dechant, Yang-Hui He +3
Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scat…
Cluster structures for the singularity
Jenny August, Man-Wai Cheung, Eleonore Faber +2
We study a category of -graded MCM modules over the curve singularity and demonstrate it has infinite type cluster combinatorics. In part…
Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
Sam Bardwell-Evans, Man-Wai Mandy Cheung, Hansol Hong +1
We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagra…
Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras
Man-Wai Mandy Cheung, Elizabeth Kelley, Gregg Musiker
We give a construction of generalized cluster varieties and generalized cluster scattering diagrams for reciprocal generalized cluster algebras, the latter of which were defined by…
Some Examples of Family Floer Mirrors
Man-Wai Mandy Cheung, Yu-Shen Lin
In this article, we give explicit calculations for the family Floer mirrors of some non-compact Calabi-Yau surfaces. We compare it with the mirror construction of Gross-Hacking-Kee…
Algebraic and symplectic viewpoint on compactifications of two-dimensional cluster varieties of finite type
Man-Wai Mandy Cheung, Renato Vianna
In this article we explore compactifications of cluster varieties of finite type in complex dimension two. Cluster varieties can be viewed as the spec of a ring generated by theta…
Categories for Grassmannian cluster algebras of infinite rank
Jenny August, Man-Wai Cheung, Eleonore Faber +2
We construct Grassmannian categories of infinite rank, providing an infinite analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. Each Grassmannian c…
Quantization of deformed cluster Poisson varieties
Man-Wai Mandy Cheung, Juan Bosco Frías-Medina, Timothy Magee
Fock and Goncharov described a quantization of cluster -varieties (also known as cluster Poisson varieties) in [FG09]. Meanwhile, families of deformations of cluster $…
Compactifications of cluster varieties and convexity
Man-Wai Cheung, Timothy Magee, Alfredo Nájera Chávez
In [GHKK18], Gross-Hacking-Keel-Kontsevich discuss compactifications of cluster varieties from "positive subsets" in the real tropicalization of the mirror. To be more precise, let…
Theta functions and quiver Grassmannians
Man-Wai Cheung
In this article, we use the relationship between cluster scattering diagrams and stability scattering diagrams to relate quiver representations with these diagrams. With a notion o…
The Model Orbit in
Man-Wai Cheung
In this article, we decompose the ring of regular functions on the nilpotent orbit of dimension 8 for the complex in which every irreducible representation of appears e…
Donaldson-Thomas invariants from tropical disks
Man-Wai Cheung, Travis Mandel
We prove that the quantum DT invariants associated to quivers with genteel potential can be expressed in terms of certain refined counts of tropical disks. This is based on a quant…
Symmetrizing Tableaux and the 5th case of the Foulkes Conjecture
Man-Wai Cheung, Christian Ikenmeyer, Sevak Mkrtchyan
The Foulkes conjecture states that the multiplicities in the plethysm Sym^a(Sym^b V) are at most as large as the multiplicities in the plethysm Sym^b(Sym^a V) for all a <= b. This…
The greedy basis equals the theta basis
Man Wai Cheung, Mark Gross, Greg Muller +4
We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.
Faithful realizability of tropical curves
Man-Wai Cheung, Lorenzo Fantini, Jennifer Park +1
We study whether a given tropical curve in can be realized as the tropicalization of an algebraic curve whose non-archimedean skeleton is faithfully represented…
Ricci flow and curvature on the variety of flags on the two dimensional projective space over the complexes, quaternions and the octonions
Man-Wai Cheung, Nolan R. Wallach
For homogeneous metrics on the spaces of the title it is shown that the Ricci flow can move a metric of stricly positive sectional curvature to one with some negative sectional cur…