33 citations · 295 across the 37 of their papers we have counts for
12 papers · 1 filter
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…
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…
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…
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…
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…
Open Gromov-Witten invariants and SYZ under local conifold transitions
Siu-Cheong Lau
For a local Calabi-Yau manifold which is a smoothing of toric Gorenstein singularity, this paper computes the open Gromov-Witten invariants of a generic fiber of the special Lagran…
Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces
Kwokwai Chan, Siu-Cheong Lau
In this paper, we compute the open Gromov-Witten invariants for every compact toric surface X which is semi-Fano (i.e. the anticanonical line bundle is nef). Unlike the Fano case,…
A relation for Gromov-Witten invariants of local Calabi-Yau threefolds
Siu-Cheong Lau, Naichung Conan Leung, Baosen Wu
We compute certain open Gromov-Witten invariants for toric Calabi-Yau threefolds. The proof relies on a relation for ordinary Gromov-Witten invariants for threefolds under certain…