53 citations · 434 across the 46 of their papers we have counts for
46 papers
Brane quantization and SYZ mirror symmetry
Kwokwai Chan, Naichung Conan Leung, Qin Li +2
Coisotropic A-branes were introduced by Kapustin--Orlov to enlarge the Fukaya category of a symplectic manifold in a way that aligns with predictions from homological mirror symmet…
Iwahori-Coulomb branches, stable envelopes, and quantum cohomology of cotangent bundles of flag varieties
Ki Fung Chan, Kwokwai Chan, Chi Hong Chow +1
We consider Iwahori-Coulomb branches , which are the affine flag analogs of the original Coulomb branches $\mathcal{A}_{G,\math…
Quantization of Kähler manifolds via differential operators
Kwokwai Chan, Naichung Conan Leung, Qin Li +1
In this paper, we study the quantization of classical observables (i.e., functions) on a Kähler manifold as differential operators acting on holomorphic sections of tensor powe…
Quantum cohomology, shift operators, and Coulomb branches
Ki Fung Chan, Kwokwai Chan, Chin Hang Eddie Lam
Given a complex reductive group and a -representation , there is an associated Coulomb branch algebra defined by Braverman, Fi…
A perturbative construction of primitive forms from log Landau-Ginzburg mirrors of toric manifolds
Kwokwai Chan, Ziming Nikolas Ma, Hao Wen
We introduce the notion of a logarithmic Landau-Ginzburg (log LG) model, which is essentially given by equipping the central degenerate fiber of the family of Landau-Ginzburg (LG)…
Quantizable functions on Kähler manifolds and non-formal quantization
Kwokwai Chan, Naichung Conan Leung, Qin Li
Applying the Fedosov connections constructed in our previous work, we find a (dense) subsheaf of smooth functions on a Kähler manifold which admits a non-formal deformation qua…
From deformation theory to tropical geometry
Kwokwai Chan
This is a write-up of the author's invited talk at the Eighth International Congress of Chinese Mathematicians (ICCM) held at Beijing in June 2019. We give a survey on joint works…
Smoothing, scattering, and a conjecture of Fukaya
Kwokwai Chan, Naichung Conan Leung, Ziming Nikolas Ma
In 2002, Fukaya proposed a remarkable explanation of mirror symmetry detailing the SYZ conjecture by introducing two correspondences: one between the theory of pseudo-holomorphic c…
Quantization of Kähler manifolds
Kwokwai Chan, Naichung Conan Leung, Qin Li
This is a survey on our recent works which reveal new relationships among deformation quantization, geometric quantization, Berezin-Toeplitz quantization and BV quantization on Käh…
Bargmann-Fock sheaves on Kähler manifolds
Kwokwai Chan, Naichung Conan Leung, Qin Li
Fedosov used flat sections of the Weyl bundle on a symplectic manifold to construct a star product which gives rise to a deformation quantization. By extending Fedosov's me…
Kapranov's structures, Fedosov's star products, and one-loop exact BV quantizations on Kähler manifolds
Kwokwai Chan, Naichung Conan Leung, Qin Li
We study quantization schemes on a Kähler manifold and relate several interesting structures. We first construct Fedosov's star products on a Kähler manifold as quantizations o…
Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces
Kwokwai Chan, Ziming Nikolas Ma, Yat-Hin Suen
We introduce the notion of tropical Lagrangian multi-sections over a -dimensional integral affine manifold with singularities, and use them to study the reconstruction probl…
A geometric construction of representations of the Berezin-Toeplitz quantization
Kwokwai Chan, Naichung Conan Leung, Qin Li
For a Kähler manifold equipped with a prequantum line bundle , we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantizati…
Smoothing pairs over degenerate Calabi-Yau varieties
Kwokwai Chan, Ziming Nikolas Ma
We apply the techniques developed in our previous work with Leung to study smoothings of a pair , where is a bounded perfect complex of locally…
Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties
Kwokwai Chan, Naichung Conan Leung, Ziming Nikolas Ma
Given a degenerate Calabi-Yau variety equipped with local deformation data, we construct an almost differential graded Batalin-Vilkovisky (dgBV) algebra , producin…
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…
Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties
Kwokwai Chan, Naichung Conan Leung, Changzheng Li
We construct pseudotoric structures (à la Tyurin) on the two-step flag variety , and explain a general relation between pseudotoric structures and special Lagran…
Geometric quantization via SYZ transforms
Kwokwai Chan, Yat-Hin Suen
The so-called quantization problem in geometric quantization is asking whether the space of wave functions is independent of the choice of polarization. In this paper, we apply SYZ…
Tropical counting from asymptotic analysis on Maurer-Cartan equations
Kwokwai Chan, Ziming Nikolas Ma
Let be a toric surface and be its Landau-Ginzburg (LG) mirror where is the Hori-Vafa potential. We apply asymptotic analysis to study the extended de…
Scattering diagrams from asymptotic analysis on Maurer-Cartan equations
Kwokwai Chan, Naichung Conan Leung, Ziming Nikolas Ma
Let be a semi-flat Calabi-Yau manifold equipped with a Lagrangian torus fibration . We investigate the asymptotic behavior of M…
SYZ transforms for immersed Lagrangian multi-sections
Kwokwai Chan, Yat-Hin Suen
In this paper, we study the geometry of the SYZ transform on a semi-flat Lagrangian torus fibration. Our starting point is an investigation on the relation between Lagrangian surge…
Quasimap SYZ for toric Calabi-Yau manifolds
Kwokwai Chan
In this note, we study the SYZ mirror construction for a toric Calabi-Yau manifold using instanton corrections coming from Woodward's quasimap Floer theory instead of Fukaya-Oh-Oht…
Homological mirror symmetry for local Calabi-Yau manifolds via SYZ
Kwokwai Chan
This is a write-up of the author's talk in the conference "Algebraic Geometry in East Asia 2016" held at the University of Tokyo in January 2016. We give a survey on a series of pa…
Lagrangian sections on mirrors of toric Calabi-Yau 3-folds
Kwokwai Chan, Daniel Pomerleano, Kazushi Ueda
We construct Lagrangian sections of a Lagrangian torus fibration on a 3-dimensional conic bundle, which are SYZ dual to holomorphic line bundles over the mirror toric Calabi-Yau 3-…