Papers

Preprints

• K. Chan, Z. N. Ma and H. Wen, A perturbative construction of primitive forms from log Landau-Ginzburg mirrors of toric manifolds, preprint (2023).
  
• K. Chan, N. C. Leung and Z. N. Ma, Smoothing, scattering, and a conjecture of Fukaya, preprint (2022).
• K. Chan, D. Pomerleano and K. Ueda, Lagrangian sections on mirrors of toric Calabi-Yau 3-folds, preprint (2016).

Accepted/Published

• K. Chan, From deformation theory to tropical geometry, in "Proceedings of the Eighth International Congress of Chinese Mathematicians", to appear.
• 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 dim_C H^q(X_t,E_t), 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 A_n-singularities, Commun. Number Theory Phys. 7 (2013), no. 2, 361-396.
• K. Chan, Homological mirror symmetry for A_n-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.