As announced in Gross and Siebert (in Algebraic geometry: Salt Lake City 2015,
Proceedings of Symposia in Pure Mathematics, vol 97, no 2. AMS, Providence, pp 199–230 …

Let Y be a (partial) minimal model of a scheme V with a cluster structure (of type A, X or of a
quotient of A or a fibre of X). Under natural assumptions, for every choice of seed we …

We study the relation between the integer tropical points of a cluster variety (satisfying the
full Fock-Goncharov conjecture) and the totally positive part of the tropicalization of an ideal …

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 …

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 …

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 …

Fock and Goncharov described a quantization of cluster X-varieties (also known as cluster
Poisson varieties) in Fock and Goncharov (Ann. Sci. Éc. Norm. Supér. 42 (6), 865–930) …

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-Keel for …

We extend the notion of y-variables (coefficients) in cluster algebras to cluster scattering
diagrams (CSDs). Accordingly, we extend the dilogarithm identity associated with a period in …

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 …