33 citations · 295 across the 37 of their papers we have counts for
37 papers
Disk potential functions for polygon spaces
Yoosik Kim, Siu-Cheong Lau, Xiao Zheng
We derive a Floer theoretical SYZ mirror for an equilateral and generic polygon space. The disk potential function of the monotone torus fiber of the caterpillar bending system is…
Mirror Symmetry for Quiver Algebroid Stacks
Siu-Cheong Lau, Junzheng Nan, Ju Tan
In this paper, we provide a new construction of quiver algebroid stacks and the associated mirror functors for symplectic manifolds. First, we formulate the concept of a quiver sta…
SYZ mirror symmetry for del Pezzo surfaces and affine structures
Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin
We prove that the Landau--Ginzburg superpotential of del Pezzo surfaces can be realized as a limit of their hyperKähler rotation toward the large complex structure limit point. As…
Quantum Finite Automata and Quiver Algebras
George Jeffreys, Siu-Cheong Lau
We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the a…
Noncommutative Geometry of Computational Models and Uniformization for Framed Quiver Varieties
George Jeffreys, Siu-Cheong Lau
We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of th…
Kähler Geometry of Quiver Varieties and Machine Learning
George Jeffreys, Siu-Cheong Lau
We develop an algebro-geometric formulation for neural networks in machine learning using the moduli space of framed quiver representations. We find natural Hermitian metrics on th…
On the Complex Affine Structures of SYZ Fibration of Del Pezzo Surfaces
Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin
Given any smooth cubic curve , we show that the complex affine structure of the special Lagrangian fibration of constructed by Co…
Big Quantum cohomology of orbifold spheres
Lino Amorim, Cheol-Hyun Cho, Hansol Hong +1
We construct a Kodaira-Spencer map from the big quantum cohomology of a sphere with three orbifold points to the Jacobian ring of the mirror Landau-Ginzburg potential function. Thi…
-equivariant disc potentials for toric Calabi-Yau manifolds
Hansol Hong, Yoosik Kim, Siu-Cheong Lau +1
We study the equivariant disc potentials for immersed SYZ fibers in toric Calabi-Yau manifolds. The immersed Lagrangians play a crucial role in the partial compactification of the…
-equivariant disc potential and SYZ mirror construction
Yoosik Kim, Siu-Cheong Lau, Xiao Zheng
We develop a -equivariant Lagrangian Floer theory and obtain a curved algebra, and in particular a -equivariant disc potential. We construct a Morse model, which c…
A Note on Disk Counting in Toric Orbifolds
Kwokwai Chan, Cheol-Hyun Cho, Siu-Cheong Lau +2
We compute orbi-disk invariants of compact Gorenstein semi-Fano toric orbifolds by extending the method used for toric Calabi-Yau orbifolds. As a consequence the orbi-disc potentia…
Gluing Localized Mirror Functors
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
We develop a method of gluing the local mirrors and functors constructed from immersed Lagrangians in the same deformation class. As a result, we obtain a global mirror geometry an…
Immersed two-spheres and SYZ with Application to Grassmannians
Hansol Hong, Yoosik Kim, Siu-Cheong Lau
We develop a Floer theoretical gluing technique and apply it to deal with the most generic singular fiber in the SYZ program, namely the product of a torus with the immersed two-sp…
SYZ mirror symmetry for hypertoric varieties
Siu-Cheong Lau, Xiao Zheng
We construct a Lagrangian torus fibration on a smooth hypertoric variety and a corresponding SYZ mirror variety using -duality and generating functions of open Gromov-Witten inv…
Affine elliptic surfaces with type-A singularities and orbi-conifolds
Siu Cheong Lau
Following the work of Castano-Bernard and Matessi on conifold transition in the Gross-Siebert program, we construct orbi-conifold transitions of the Shoen's Calabi-Yau threefold an…
Moduli of Lagrangian immersions with formal deformations
Hansol Hong, Siu-Cheong Lau
We introduce a joint project with Cheol-Hyun Cho on the construction of quantum-corrected moduli of Lagrangian immersions. The construction has important applications to mirror sym…
Mirror of Atiyah flop in symplectic geometry and stability conditions
Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau +1
We study the mirror operation of the Atiyah flop in symplectic geometry. We formulate the operation for a symplectic manifold with a Lagrangian fibration. Furthermore we construct…
Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry
Atsushi Kanazawa, Siu-Cheong Lau
We carry out the SYZ program for the local Calabi--Yau manifolds of type by developing an equivariant SYZ theory for the toric Calabi--Yau manifolds of infinite-typ…
Noncommutative homological mirror functor
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with a natural f…
Geometric transitions and SYZ mirror symmetry
Atsushi Kanazawa, Siu-Cheong Lau
We prove that the punctured generalized conifolds and punctured orbifolded conifolds are mirror symmetric under the SYZ program with quantum corrections. This mathematically confir…
Modularity of Open Gromov-Witten Potentials of Elliptic Orbifolds
Siu-Cheong Lau, Jie Zhou
We study the modularity of the genus zero open Gromov-Witten potentials and its generating matrix factorizations for elliptic orbifolds. These objects constructed by Lagrangian Flo…
Non-Kaehler SYZ mirror symmetry
Siu-Cheong Lau, Li-Sheng Tseng, Shing-Tung Yau
We study SYZ mirror symmetry in the context of non-Kaehler Calabi-Yau manifolds. In particular, we study the six-dimensional Type II supersymmetric systems with Ramond-Ramo…
Localized mirror functor constructed from a Lagrangian torus
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we define a holomorphic function W known as the Floer potential. We construct a canonical A-infinity funct…
Gross-Siebert's slab functions and open GW invariants for toric Calabi-Yau manifolds
Siu-Cheong Lau
This paper derives an equality between the slab functions in Gross-Siebert program and generating functions of open Gromov-Witten invariants for toric Calabi-Yau manifolds, and the…