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 …

Abstract Gross–Hacking–Keel–Kontsevich discuss compactifications of cluster varieties from
positive subsets in the real tropicalization of the mirror. To be more precise, let be the …

We prove a conjecture of Bousseau, van Garrel and the first-named author relating, under
suitable positivity conditions, the higher genus maximal contact log Gromov-Witten …

We show that the ring of regular functions of every smooth affine log Calabi-Yau surface with
maximal boundary has a vector space basis parametrized by its set of integer tropical points …

We classify rank $2 $ cluster varieties (those for which the span of the rows of the exchange
matrix is $2 $-dimensional) according to the deformation type of a generic fiber $ U $ of their …

This thesis explores different aspects of Gromov–Witten theory and is divided into two parts.
The first investigates conjectures of Bousseau, Brini and van Garrel relating three a priori …

We construct the mirror algebra to a smooth affine log Calabi-Yau variety with maximal
boundary, as the spectrum of a commutative associative algebra with a canonical basis …

A log Calabi–Yau surface with maximal boundary, or Looijenga pair, is a pair (Y, D) with Y a
smooth rational projective complex surface and D= D 1+⋯+ D l∈|− KY| an anticanonical …

arXiv:2405.02735v1 [math.AG] 4 May 2024 Tropical methods for stable Horikawa surfaces
Page 1 arXiv:2405.02735v1 [math.AG] 4 May 2024 Tropical methods for stable Horikawa …

The 2-dimensional Lyness map is a 5-periodic birational map of the plane which may
famously be resolved to give an automorphism of a log Calabi–Yau surface, given by the …