For a large class of maximally degenerate families of Calabi–Yau hypersurfaces of complex
projective space, we study non-Archimedean and tropical Monge–Ampère equations, taking …

We show that the underlying complex manifold of a complete non-compact two-dimensional
shrinking gradient Kähler–Ricci soliton. M; g; X/with soliton metric g with bounded scalar …

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 …

We construct special Lagrangian 3-spheres in non-Kähler compact threefolds equipped with
the Fu–Li–Yau geometry. These non-Kähler geometries emerge from topological transitions …

Given a smooth log Calabi–Yau pair (X, D), we use the intrinsic mirror symmetry construction
to define the mirror proper Landau–Ginzburg potential and show that it is a generating …

Let $(S, E) $ be a log Calabi-Yau surface pair with $ E $ a smooth divisor. We define new
conjecturally integer-valued counts of $\mathbb {A}^ 1$-curves in $(S, E) $. These log BPS …

We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror
symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some …

We construct new complete Calabi–Yau metrics on the complement of an anticanonical
divisor D in a Fano manifold of dimension at least three, when D consists of two transversely …

We give a mathematically precise statement of the SYZ conjecture between mirror space
pairs and prove it for any toric Calabi-Yau manifold with the Gross Lagrangian fibration. To …

We prove the Strominger-Yau-Zaslow mirror symmetry conjecture for non-compact Calabi-
Yau surfaces arising from, on the one hand, pairs $(\check {Y},\check {D}) $ of a del Pezzo …