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 give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a
“torus”. We show that our definition is equivalent to the one of Borisov, Chen and Smith in …

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 …

We develop a topological vertex formalism for computing the Donaldson–Thomas invariants
of Calabi–Yau orbifolds. The basic combinatorial object is the orbifold vertex VλμνG, a …

We develop an analogue of Eisenbud–Fløystad–Schreyer's Tate resolutions for toric
varieties. Our construction, which is given by a noncommutative analogue of a Fourier …

We develop a new approach to the study of supersymmetric gauge theories on ALE spaces
using the theory of framed sheaves on root toric stacks, which illuminates relations with …

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 …

We study the generalized hypergeometric system introduced by Gelfand, Kapranov and
Zelevinsky and its relationship with the toric Deligne–Mumford (DM) stacks recently studied …

We prove that every spherical object in the derived Fukaya category of a closed surface of
genus at least whose Chern character represents a nonzero Hochschild homology class is …