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 …

A complete embedding is a symplectic embedding are bounded, we deduce the same result
for relative symplectic cohomology. We introduce a technique for constructing complete …

Cluster varieties come in pairs: for any 𝒳 cluster variety there is an associated Fock–
Goncharov dual 𝒜 cluster variety. On the other hand, in the context of mirror symmetry …

This survey covers recent developments on the geometry and physics of Looijenga pairs,
namely pairs (X, D) with X a complex algebraic surface and D a singular anticanonical …

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 study webs of 5-branes with 7-branes in Type IIB string theory from a geometric
perspective. To any such a web $ W $, we attach a log Calabi-Yau surface $(Y, D) $ with a …

We study the Landau-Ginzburg mirror of toric/non-toric blowups of (possibly non-Fano) toric
surfaces arising from SYZ mirror symmetry. Through the framework of tropical geometry, we …

In 2002, Fukaya proposed a remarkable explanation of mirror symmetry detailing the SYZ
conjecture by introducing two correspondences: one between the theory of pseudo …

We derive a Floer theoretical SYZ mirror for an equilateral and generic polygon space. The
disk potential function of the monotone torus fiber of the caterpillar bending system is …

We begin developing a theory of morphisms of moduli spaces of pseudoholomorphic curves
and discs with Lagrangian boundary conditions as Kuranishi spaces, using a modification of …