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SYZ mirror symmetry for toric Calabi-Yau manifolds

- Kwokwai Chan, Siu-Cheong Lau, N. Leung
- Mathematics, Physics
- 19 June 2010

We investigate mirror symmetry for toric Calabi-Yau manifolds from the perspective of the SYZ conjecture. Starting with a non-toric special Lagrangian torus fibration on a toric Calabi-Yau manifold… Expand

Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties

- Kwokwai Chan, N. Leung, Z. Ma
- Mathematics
- 28 February 2019

Given a degenerate Calabi-Yau variety X equipped with local deformation data, we construct an almost differential graded Batalin-Vilkovisky (almost dgBV) algebra PV(X), giving a singular version of… Expand

Homological mirror symmetry for An-resolutions as a T-duality

- Kwokwai Chan
- Mathematics, Computer Science
- J. Lond. Math. Soc.
- 5 December 2011

TLDR

Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces

- Kwokwai Chan, Siu-Cheong Lau
- Mathematics
- 25 October 2010

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, this involves… Expand

Lagrangian Torus Fibrations and Homological Mirror Symmetry for the Conifold

- Kwokwai Chan, Daniel Pomerleano, K. Ueda
- Physics, Mathematics
- 4 May 2013

We discuss homological mirror symmetry for the conifold from the point of view of the Strominger–Yau–Zaslow conjecture.

Dual torus fibrations and homological mirror symmetry for $A_n$-singularities

- Kwokwai Chan, K. Ueda
- Mathematics
- 2 October 2012

We study homological mirror symmetry for not necessarily compactly supported coherent sheaves on the minimal resolutions of A_n-singularities. An emphasis is put on the relation with the… Expand

Scattering diagrams from asymptotic analysis on Maurer–Cartan equations

- Kwokwai Chan, N. Leung, Z. Ma
- Mathematics, Physics
- Journal of the European Mathematical Society
- 21 July 2018

We investigate SYZ mirror symmetry via asymptotic analysis on Maurer-Cartan equations, following a program set forth by Fukaya. Let $X_0$ and $\check{X}_0$ be a mirror pair of semi-flat Calabi-Yau… Expand

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

- Kwokwai Chan, Cheol-hyun Cho, Siu-Cheong Lau, Hsian-hua Tseng
- Mathematics, Physics
- 3 June 2013

Given a toric Calabi-Yau orbifold X whose underlying toric variety is semi- projective, we construct and study a non-toric Lagrangian torus bration on X , which we call the Gross bration. We apply… Expand

Mirror symmetry for toric Fano manifolds via SYZ transformations

- Kwokwai Chan, N. Leung
- Mathematics
- 18 January 2008

Abstract We construct and apply Strominger–Yau–Zaslow mirror transformations to understand the geometry of the mirror symmetry between toric Fano manifolds and Landau–Ginzburg models.

The Ooguri-Vafa metric, holomorphic discs and wall-crossing

- Kwokwai Chan
- Mathematics
- 19 September 2009

Recently, Gaiotto, Moore and Neitzke \cite{GMN08} proposed a new construction of hyperk\"{a}hler metrics. In particular, they gave a new construction of the Ooguri-Vafa metric, in which they came… Expand

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