Faculty
My research interest lies in the fields of Complex Geometry, Symplectic Geometry, Mathematical Physics, with special emphasis on Mirror Symmetry, which is a mysterious duality between symplectic geometry (A-model) of a Calabi-Yau manifold X and complex geometry (B-model) of its mirror Calabi-Yau manifold Xˇ. The focus of my current research is to unveil mysteries in Mirror Symmetry with viewpoint from the Strominger-Yau-Zaslow proposal.
Publications
11. Tropical Lagrangian multi-sections and smoothing of locally free sheaves on degenerated Calabi-Yau surfaces, (with K. W. Chan and Y. H. Suen) submitted.
10. Smoothing Pairs Over Degenerate Calabi–Yau Varieties (with K. W. Chan), International Mathematics Research Notices , rnaa212, 2020, https://doi.org/10.1093/imrn/rnaa212 .
9. Geometry of Maurer-Cartan equation near degenerate Calabi-Yaus (with K. W. Chan And N. C. Leung), accepted for publication in Journal of Differential Geometry.
8. Fukaya's conjecture on $S^1$-equivariant de Rham complex, submitted.
7. Fukaya's conjecture on Witten's twisted A_\infty structures, with Kaileung Chan and Naichung Conan Leung, J. Differential Geom. 118(3): 399-455 (July 2021). DOI: 10.4310/jdg/1625860622 .
6. Scattering diagram from asymptotic analysis on Maurer-Cartan equations, with Kwokwai Chan and Naichung Conan Leung, Journal of the European Mathematical Society, 2021, DOI: 10.4171/JEMS/1100.
5. Tropical counting from asymptotic analysis on Maurer-Cartan equations, with Kwokwai Chan, Transactions of the American Mathematical Society, 2020, https://doi.org/10.1090/tran/8128.
4. Theta functions from asymptotic analysis on Maurer-Cartan equations, with Matthew Bruce Young and Naichung Conan Leung, International Mathematics Research Notices, rnz220, 2019, https://doi.org/10.1093/imrn/rnz220.
3. SYZ mirror symmetry from Witten-Morse theory, to be appeared in CMA proceedings.
2. Lattice points counting via Einstein metrics, with Naichung Conan Leung, Journal of Differential geometry 92 (2012), no. 1, 55-69.
1. Flat branes on tori and Fourier transform in the SYZ programme, with Kaileung Chan and Naichung Conan Leung, Proceedings of the G"okova Geometry-Topology Conference (2011), page 1-31, International press.