We introduce an integral structure in orbifold quantum cohomology associated to the K-
group and the Γˆ-class. In the case of compact toric orbifolds, we show that this integral …

We propose Gamma conjectures for Fano manifolds which can be thought of as a square
root of the index theorem. Studying the exponential asymptotics of solutions to the quantum …

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus
zero and after an analytic continuation, the quantum singularity theory (FJRW theory) …

Let X be a Gorenstein orbifold with projective coarse moduli space X and let Y be a crepant
resolution of X. We state a conjecture relating the genus-zero Gromov–Witten invariants of X …

Let X and Y be K-equivalent toric Deligne–Mumford stacks related by a single toric wall-
crossing. We prove the Crepant Transformation Conjecture in this case, fully-equivariantly …

Hodge theoretic mirror symmetry is concerned with the equivalence of Hodge structures
from symplectic geometry (A-model or Gromov-Witten theory) of Y and complex geometry (B …

For a toric Calabi–Yau (CY) orbifold $\mathcal {X} $ whose underlying toric variety is semi-
projective, we construct and study a non-toric Lagrangian torus fibration on $\mathcal {X} …

We construct full strong exceptional collections of line bundles on smooth toric Fano Deligne–
Mumford stacks of Picard number at most two and of any Picard number in dimension two. It …

The asymptotic behaviour of solutions to the quantum differential equation of a Fano
manifold F defines a characteristic class AF of F, called the principal asymptotic class …

We give a pedagogical review of the computation of Gromov–Witten invariants via
localization in 2D gauged linear sigma models. We explain the relationship between the two …