# Applications of homological mirror symmetry to hypergeometric systems: duality conjectures

@article{Borisov2013ApplicationsOH, title={Applications of homological mirror symmetry to hypergeometric systems: duality conjectures}, author={Lev Borisov and Richard Paul Horja}, journal={arXiv: Algebraic Geometry}, year={2013} }

## 8 Citations

On duality of certain GKZ hypergeometric systems

- MathematicsAsian Journal of Mathematics
- 2021

We study a pair of conjectures on better behaved GKZ hypergeometric systems of PDEs inspired by Homological mirror symmetry for crepant resolutions of Gorenstein toric singularities. We prove the…

Narrow quantum D-modules and quantum Serre duality

- MathematicsAnnales de l'Institut Fourier
- 2021

Given Y a non-compact manifold or orbifold, we define a natural subspace of the cohomology of Y called the narrow cohomology. We show that despite Y being non-compact, there is a well-defined and…

Towards a mirror theorem for GLSMs

- Mathematics
- 2021

We propose a method for computing generating functions of genus-zero invariants of a gauged linear sigma model (V, G, θ, w). We show that certain derivatives of I-functions of quasimap invariants of…

Quantum Serre theorem as a duality between quantum D-modules

- Mathematics, Physics
- 2016

We give an interpretation of quantum Serre theorem of Coates and Givental as a duality of twisted quantum D-modules. This interpretation admits a non-equivariant limit, and we obtain a precise…

Extremal transitions via quantum Serre duality

- Mathematics
- 2020

Two varieties $Z$ and $\widetilde Z$ are said to be related by extremal transition if there exists a degeneration from $Z$ to a singular variety $\overline Z$ and a crepant resolution $\widetilde Z…

Brane transport beyond Calabi-Yau: a tale of geometry and localization

- Mathematics
- 2019

The goal of this thesis is to study the behavior of branes preserving B-type supersymmetry in two-dimensional N = (2,2) theories as parameters are varied across the (quantum-corrected) Kahler moduli…

Brane transport in anomalous (2,2) models and localization

- Physics
- 2018

We study B-branes in two-dimensional N=(2,2) anomalous models, and their behaviour as we vary bulk parameters in the quantum Kahler moduli space. We focus on the case of (2,2) theories defined by…

Variation of GIT and Variation of Lagrangian Skeletons II: Quasi-Symmetric Case

- Mathematics
- 2020

Consider $(\mathbb{C}^*)^k$ acting on $\mathbb{C}^N$ satisfying certain 'quasi-symmetric' condition which produces a class of toric Calabi-Yau GIT quotient stacks. Using subcategories of…

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