Hsian-Hua Tseng

Wall-crossings in toric Gromov-Witten theory I: crepant examples

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 to those of Y , which differs in general from the Crepant Resolution Conjectures of Ruan and Bryan‐Graber, and prove our conjecture when XD P.1;1;2/ and XD P.1;1;1;3/. As a consequence, we see that the original form of the Bryan‐Graber Conjecture holds for P.1;1;2/ but is probably false for P.1;1;1;3/. Our methods are based on mirror symmetry for toric orbifolds. 53D45; 14N35, 83E30

A mirror theorem for toric stacks

We prove a Givental-style mirror theorem for toric Deligne–Mumford stacks

The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies

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Gross fibrations, SYZ mirror symmetry, and open Gromov–Witten invariants for toric Calabi–Yau orbifolds

. This determines the genus-zero Gromov–Witten invariants of

Orbifold cup products and ring structures on Hochschild cohomologies

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On the global quotient structure of the space of twisted stable maps to a quotient stack

in terms of an explicit hypergeometric function, called the

On Donaldson-Thomas invariants of threefold stacks and gerbes

I

The orbifold Chow ring of hypertoric Deligne-Mumford stacks

-function, that takes values in the Chen–Ruan orbifold cohomology of

Lagrangian Floer Superpotentials and Crepant Resolutions for Toric Orbifolds

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Gromov–Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda hierarchies

.