We show that a purely algebraic structure, a two-dimensional scattering diagram, describes
a large part of the wall-crossing behavior of moduli spaces of Bridgeland semistable objects …

We explore connections between three structures associated with the cohomology of the
moduli of 1-dimensional stable sheaves on P 2: perverse filtrations, tautological classes, and …

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+\dots+ D_l\in|-K_Y| $ an …

We explore the structure of the cohomology ring of the moduli space of stable 1-dimensional
sheaves on $\mathbb {P}^ 2$ of any degree. We obtain a minimal set of tautological …

The spectrum of BPS states in type IIA string theory compactified on a Calabi–Yau threefold
famously jumps across codimension-one walls in complexified Kähler moduli space, leading …

Choosing a normal crossings anticanonical divisor of $\mathbb {P}^ 2$ leads to four log
Calabi-Yau surfaces, three of which are Looijenga pairs. In this survey article, I describe how …

Consider a log Calabi-Yau pair $(X, D) $ consisting of a smooth del Pezzo surface $ X $ of
degree $\geq 3$ and a smooth anticanonical divisor $ D $. We prove a correspondence …

We conjecture that the generating series of Gromov-Witten invariants of the Hilbert schemes
of $ n $ points on a K3 surface are quasi-Jacobi forms and satisfy a holomorphic anomaly …

The mirror dual of a smooth toric Fano surface X equipped with an anticanonical divisor E is
a Landau–Ginzburg model with superpotential, W. Carl–Pumperla–Siebert give a definition …

In, we established a series of correspondences relating five enumerative theories of log
Calabi–Yau surfaces, ie pairs (Y, D) with Y a smooth projective complex surface and D= D …