Papers
Preprints
Accepted/Published
- K.
Chan, N. C. Leung and Z. N. Ma, Smoothing, scattering, and a conjecture of Fukaya, Forum Math. Pi 13 (2025), Paper No. e7.
- K. Chan, From deformation theory to tropical geometry, in "Proceedings
of the International Consortium of Chinese Mathematicians 2019", Vol. 2, Int.
Press, Somerville, MA, 2024.
- K.
Chan, N. C. Leung and Z. N. Ma, Geometry
of the Maurer-Cartan equation near degenerate Calabi-Yau varieties,
J. Differential Geom. 125 (2023), no. 1, 1-84.
- K.
Chan, N. C. Leung and Q. Li, Quantizable functions on Kaehler manifolds and non-formal quantization, Adv.
Math. 433 (2023), 109293, 34 pp.
- K.
Chan, N. C. Leung and Q. Li, A
geometric construction of representations of the Berezin-Toeplitz
quantization, Adv. Theor. Math.
Phys. 26 (2022), no. 1, 1-36.
- K.
Chan, N. C. Leung and Q. Li, Kapranov's L∞
structures, Fedosov's star products and one-loop exact BV
quantizations on Kaehler
manifolds, Commun. Number Theory Phys. 16 (2022), no. 2, 299-351.
- K. Chan, N. C. Leung and Z. N.
Ma, Scattering diagrams from
asymptotic analysis on Maurer-Cartan equations, J.
Eur. Math. Soc. (JEMS) 24 (2022), no. 3, 773-849.
- K.
Chan, Z. N. Ma and Y.-H. Suen, Tropical
Lagrangian multi-sections and smoothing of locally free sheaves over
degenerate Calabi-Yau surfaces, Adv.
Math. 401 (2022), 108280, 37 pp.
- K.
Chan and Z. N. Ma, Smoothing
pairs over degenerate Calabi-Yau varieties, Int.
Math. Res.
Not. IMRN 2022 (2022), no. 4, 2582-2614.
- K.
Chan, N. C. Leung and Q. Li, Bargmann-Fock sheaves on Kaehler
manifolds, Comm. Math. Phys. 388 (2021), no. 3, 1297-1322.
- K.
Chan, N. C. Leung and Q. Li, Quantization of Kaehler
manifolds, J.
Geom. Phys. 163 (2021), 104143, 13 pp.
- K. Chan, SYZ
mirror symmetry for toric varieties,
in "Handbook for Mirror Symmetry of Calabi-Yau and Fano
Manifolds", 1-32, Adv. Lect. Math. (ALM) 47, Int.
Press, Somerville, MA, 2020.
- K. Chan, S.-C. Lau, N. C.
Leung and H.-H. Tseng, Open Gromov-Witten invariants
and mirror maps for semi-Fano toric manifolds, Pure
Appl. Math. Q. 16 (2020),
no. 3, 675-720.
- K.
Chan and Z. N. Ma, Tropical counting from
asymptotic analysis on Maurer-Cartan equations, Trans. Amer. Math. Soc. 373
(2020), no. 9, 6411-6450.
- K.
Chan, C.-H. Cho, S.-C. Lau, N. C. Leung and H.-H. Tseng, A note on disk counting in toric
orbifolds, SIGMA Symmetry Integrability Geom.
Methods Appl. 16 (2020),
055, 15 pp.
- K.
Chan and Y.-H. Suen, Geometric
quantization via SYZ transforms, Adv. Theor. Math.
Phys. 24 (2020),
no. 1, 25-66.
- K. Chan and Y.-H. Suen, On
the jumping phenomenon of dimC Hq(Xt,Et), Asian
J. Math. 23 (2019),
no. 4, 681-702.
- K.
Chan and Y.-H. Suen, SYZ
transforms for immersed Lagrangian multi-sections, Trans.
Amer. Math. Soc. 372
(2019), no. 8, 5747-5780.
- K.
Chan, N. C. Leung and C. Li, Pseudotoric
structures and special Lagrangian torus fibrations on certain flag
varieties, J. Geom. Phys. 146
(2019), 103489, 16 pp.
- K. Chan, Quasimap
SYZ for toric Calabi-Yau manifolds, in "Proceedings
of the Seventh International Congress of Chinese Mathematicians. Vol.
II", 317-333, Adv. Lect. Math. (ALM) 44, Int. Press,
Somerville, MA, 2019.
- K. Chan, N. C. Leung and Q.
Li, BV quantization of the
Rozansky-Witten model, Comm. Math. Phys. 355
(2017) no. 1, 97-144.
- K. Chan, Homological
mirror symmetry for local Calabi-Yau manifolds via SYZ, Taiwanese J. Math. 21
(2017), no. 3, 505-529.
- K. Chan, S.-C. Lau, N. C.
Leung and H.-H. Tseng, Open
Gromov-Witten invariants,
mirror maps, and Seidel representations for toric manifolds,
Duke Math. J. 166
(2017), no. 8, 1404-1462.
- K.
Chan, A glimpse of the SYZ conjecture
and related developments, ICCM Not. 4
(2016), no. 1, 14-28.
- K. Chan, C.-H. Cho, S.-C. Lau
and H.-H. Tseng, Gross fibrations, SYZ mirror
symmetry, and open Gromov-Witten invariants for toric Calabi-Yau
orbifolds, J.
Differential Geom. 103
(2016), no. 2, 207-288.
- K. Chan and Y.-H. Suen, A differential-geometric approach
to deformations of pairs (X,E), Complex
Manifolds 3
(2016), 16-40.
- K.
Chan, D. Pomerleano and K. Ueda, Lagrangian torus fibrations and
homological mirror symmetry for the conifold, Comm. Math. Phys. 341
(2016), no. 1, 135-178.
- K.
Chan and Y.-H. Suen, A Froelicher-type inequality for
generalized complex manifolds, Ann. Global Anal. Geom. 47
(2015), no. 2, 135-145.
- K. Chan, The Strominger-Yau-Zaslow
conjecture and its impact, in "Selected Expository Works of Shing-Tung Yau
with Commentary. Vol. II", 1183-1208, Adv. Lect. Math. (ALM) 29, Int.
Press,
Somerville, MA, 2014.
- K. Chan, C.-H. Cho, S.-C. Lau
and H.-H. Tseng, Lagrangian
Floer superpotentials
and crepant resolutions for toric orbifolds,
Comm. Math. Phys. 328
(2014), no. 1, 83-130.
- K. Chan and S.-C. Lau, Open Gromov-Witten
invariants and superpotentials for semi-Fano toric surfaces,
Int. Math. Res.
Not. IMRN 2014
(2014), no. 14, 3759-3789.
- K.
Chan and K. Ueda, Dual
torus fibrations and
homological mirror symmetry for An-singularities,
Commun. Number Theory Phys. 7 (2013),
no. 2,
361-396.
- K.
Chan, Homological mirror symmetry for An-resolutions
as a T-duality,
J. Lond. Math. Soc. (2) 87
(2013), no. 1, 204-222.
- K. Chan, S.-C. Lau and H.-H.
Tseng, Enumerative meaning of mirror
maps for toric Calabi-Yau manifolds, Adv. Math. 244
(2013), 605-625.
- K. Chan, S.-C. Lau and N. C.
Leung, SYZ mirror symmetry for toric
Calabi-Yau manifolds, J.
Differential Geom. 90
(2012), no. 2, 177-250; Erratum, J.
Differential Geom. 99
(2015), no. 1, 165-167.
- K. Chan, A
formula equating open and closed Gromov-Witten invariants and its
applications to mirror symmetry, Pacific J.
Math. 254
(2011), no. 2,
275-293.
- K. Chan and N. C.
Leung, Matrix
factorizations from SYZ transformations, in
"Advances
in Geometric Analysis", 203-224, Adv. Lect. Math. (ALM) 21, Int.
Press,
Somerville, MA, 2012.
- K. Chan, The
Ooguri-Vafa metric,
holomorphic discs and
wall-crossing, Math. Res. Lett. 17
(2010), no. 3, 401-414.
- K. Chan and N. C.
Leung, On
SYZ mirror transformations, in "New
Developments in Algebraic
Geometry, Integrable Systems and Mirror Symmetry (RIMS, Kyoto,
2008)", 1-30,
Adv. Stud.
Pure Math. 59,
Math.
Soc. Japan, Tokyo, 2010.
- K. Chan and N. C.
Leung, Mirror symmetry for toric Fano
manifolds via SYZ transformations, Adv.
Math.
223
(2010), no. 3, 797-839.
- K.
Chan, Holomorphic
line bundles on
projective toric manifolds from Lagrangian sections of their mirrors by
SYZ transformations, Int. Math. Res.
Not. IMRN 2009
(2009),
no. 24, 4686-4708.
- K. Chan and N. C. Leung, Miyaoka-Yau-type
inequalities for Kaehler-Einstein
manifolds, Comm. Anal. Geom. 15
(2007), no. 2, 359-379.