Dustin Ross

Crepant resolutions and open strings

Abstract In the present paper, we formulate a Crepant Resolution Correspondence for open Gromov–Witten invariants (OCRC) of toric Lagrangian branes inside Calabi–Yau 3-orbifolds by encoding the open theories into sections of Givental’s symplectic vector space. The correspondence can be phrased as the identification of these sections via a linear morphism of Givental spaces. We deduce from this a Bryan–Graber-type statement for disk invariants, which we extend to arbitrary topologies in the Hard Lefschetz case. Motivated by ideas of Iritani, Coates–Corti–Iritani–Tseng and Ruan, we furthermore propose (1) a general form of the morphism entering the OCRC, which arises from a geometric correspondence between equivariant K-groups, and (2) an all-genus version of the OCRC for Hard Lefschetz targets. We provide a complete proof of both statements in the case of minimal resolutions of threefold A n {A_{n}} -singularities; as a necessary step of the proof we establish the all-genus closed Crepant Resolution Conjecture with descendents in its strongest form for this class of examples. Our methods rely on a new description of the quantum D-modules underlying the equivariant Gromov–Witten theory of this family of targets.

Localization and gluing of orbifold amplitudes: The Gromov-Witten orbifold vertex

We define a formalism for computing open orbifold GW invariants of [C^3/G] where G is any finite abelian group. We prove that this formalism and a suitable gluing algorithm can be used to compute GW invariants in all genera of any toric CY orbifold of dimension 3. We conjecture a correspondence with the DT orbifold vertex of Bryan-Cadman-Young.

The gerby Gopakumar–Mariño–Vafa formula

We prove a formula for certain cubic

Open Gromov-Witten theory and the crepant resolution conjecture

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Wall-crossing in genus zero Landau-Ginzburg theory

-Hodge integrals in terms of loop Schur functions. We use this identity to prove the Gromov-Witten/Donaldson-Thomas correspondence for local

Cyclic Hodge integrals and loop Schur functions

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On GW/DT and Ruan's Conjecture in All Genus for Calabi-Yau 3-Orbifolds

-gerbes over

Genus-One Mirror Symmetry in the Landau-Ginzburg Model

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Donaldson-Thomas Theory and Resolutions of Toric Transverse A-Singularities

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