15 citations · 39 across the 7 of their papers we have counts for
8 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…
Fundamentals of Broken Line Convex Geometry
Juan Bosco Frías-Medina, Timothy Magee
We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational…
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…
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…
Toric degenerations of cluster varieties and cluster duality
Lara Bossinger, Bosco Frías-Medina, Timothy Magee +1
We introduce the notion of a -pattern with coefficients and its geometric counterpart: a cluster -variety with coefficients. We use these constructions to build a f…
Littlewood-Richardson coefficients via mirror symmetry for cluster varieties
Timothy Magee
I prove that the full Fock-Goncharov conjecture holds for -- the configuration space of triples of decorated fla…
Fock-Goncharov conjecture and polyhedral cones for and base affine space
Timothy Magee
I prove several conjectures of \cite{GHKK} on the cluster structure of , which in particular imply the full Fock-Goncharov conjecture for the open double Bruhat cell $\mathca…