Kwokwai Chan

Room 212, Lady Shaw Building
Department of Mathematics
The Chinese University of Hong Kong
Shatin, N.T., Hong Kong
Phone: (852) 3943-7976
Email: kwchan_at_math.cuhk.edu.hk (with _at_ replaced by @)

Education

Ph.D. (2008), The Chinese University of Hong Kong, Advisor: Prof. Naichung Conan Leung
M.Ph. (2004), The Chinese University of Hong Kong, Advisor: Prof. Kang Zuo
B.Sc. (2002), The Chinese University of Hong Kong

Employment

08/2011 - present: Assistant Professor, Department of Mathematics, The Chinese University of Hong Kong
01/2011 - 07/2011: Project Researcher, Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo
08/2010 - 07/2011: William Hodge Fellow, Institut des Hautes Études Scientifiques (IHÉS)
08/2008 - 07/2010: Croucher Postdoctoral Fellow, Department of Mathematics, Harvard University, Mentor: Prof. Shing-Tung Yau

Teaching

Spring 2013: MATH 3423A Seminar II
Spring 2013: MATH 3040 Algebra II
Fall 2012: MATH 3030 Algebra I
Fall 2012: MATH 1520B University Math for Applications
Spring 2012: MATH 3423F Seminar II
Spring 2012: MATH 3040 Algebra II
Fall 2011: MATH 3030 Algebra I

Research Interests

Complex Algebraic Geometry, Differential Geometry and Symplectic Geometry, with special emphasis on the geometric aspects of Mirror Symmetry and other String Dualities.

Events

International Workshop on Complex Geometry, CUHK, April 18-19, 2013
Workshop on Complex Algebraic Geometry, CUHK, January 18-20, 2013
Workshop on Lie Theory and Algebraic Geometry, CUHK, November 27, 2012
Conference on Mirror Symmetry and Related Topics, KMUST, August 20-24, 2012
Conference on Calabi-Yau and G₂ Geometry, CUHK, July 19, 2012
International Workshop on Geometry and Mathematical Physics, CUHK, October 21-22, 2011

Publications & Preprints

Dual torus fibrations and homological mirror symmetry for A_n-singularities
(with K. Ueda)
Preprint 2012. [pdf] [arXiv]
Open Gromov-Witten invariants and Seidel representations for toric manifolds
(with S.-C. Lau, N.C. Leung and H.-H. Tseng)
Preprint 2012. [pdf] [arXiv]
Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds
(with C.-H. Cho, S.-C. Lau and H.-H. Tseng)
Preprint 2012. [pdf] [arXiv]
Homological mirror symmetry for A_n-resolutions as a T-duality
J. Lond. Math. Soc. (2) 87 (2013), no. 1, 204-222. [pdf] [arXiv] [journal]
Open Gromov-Witten invariants and mirror maps for semi-Fano toric manifolds
(with S.-C. Lau, N.C. Leung and H.-H. Tseng)
Preprint 2011. [pdf] [arXiv]
Enumerative meaning of mirror maps for toric Calabi-Yau manifolds
(with S.-C. Lau and H.-H. Tseng)
Preprint 2011. [pdf] [arXiv]
Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces
(with S.-C. Lau)
Int. Math. Res. Not. 2013 (2013), to appear. [pdf] [arXiv] [journal]
SYZ mirror symmetry for toric Calabi-Yau manifolds
(with S.-C. Lau and N.C. Leung)
J. Differential Geom. 90 (2012), no. 2, 177-250. [pdf] [arXiv] [journal]
A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry
Pacific J. Math. 254 (2011), no. 2, 275-293. [pdf] [arXiv] [journal]
Matrix factorizations from SYZ transformations
(with N.C. Leung)
in Advances in Geometric Analysis, 203-224, Adv. Lect. Math. (ALM) 21, Int. Press, Somerville, MA, 2012. [pdf] [arXiv] [book]
The Ooguri-Vafa metric, holomorphic discs and wall-crossing
Math. Res. Lett. 17 (2010), no. 3, 401-414. [pdf] [arXiv] [journal]
Holomorphic line bundles on projective toric manifolds from Lagrangian sections of their mirrors by SYZ transformations
Int. Math. Res. Not. 2009 (2009), no. 24, 4686-4708. [pdf] [arXiv] [journal]
On SYZ mirror transformations
(with N.C. Leung)
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. [pdf] [arXiv] [book]
Mirror symmetry for toric Fano manifolds via SYZ transformations
(with N.C. Leung)
Adv. Math. 223 (2010), no. 3, 797-839. [pdf] [arXiv] [journal]
Miyaoka-Yau type inequalities for Kähler-Einstein manifolds
(with N.C. Leung)
Comm. Anal. Geom. 15 (2007), no. 2, 359-379. [pdf] [journal]

Note: papers posted here and on the arXiv may be different from the published versions.

Selected Sildes and Online Talks

"Enumerative meaning of mirror maps for toric Calabi-Yau manifolds"
String Theory for Mathematicians, Simons Center for Geometry and Physics, SUNY Stony Brook, USA, May 2012
"Mirror symmetry, quantum corrections and SYZ"
Colloquium, CUHK, Hong Kong, February 2011
"SYZ mirror symmetry for toric manifolds"
The 5^th ICCM, Tsinghua University, Beijing, China, December 2010
"The Ooguri-Vafa metric, holomorphic discs and wall-crossing"
International Conference on Mirror Symmetry and Gromov-Witten Theory, Seoul National University, Korea, January 2010

Useful Links

Miscellaneous

PURITY of MATH:

If I were a Springer-Verlag Graduate Text in Mathematics, I would be Frank Warner's Foundations of Differentiable Manifolds and Lie Groups.

I give a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. I include differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provide a proof of the de Rham theorem via sheaf cohomology theory, and develop the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find me extremely useful.

Which Springer GTM would you be? The Springer GTM Test