Siu-Cheong Lau

MS

 

Publications

25. Quantum corrections and wall-crossing via Lagrangian intersections, to appear in ICCM Notices.

24. Mirror of Atiyah flop in symplectic geometry and stability conditions, with Yu-Wei Fan, Hansol Hong and Shing-Tung Yau, arXiv:1706.02942.

23. Generalized SYZ mirror transformation, to appear in ICCM proceedings.

22. Local Calabi-Yau manifolds of affine type A and open Yau-Zaslow formula via SYZ mirror symmetry, with Atsushi Kanazawa, arXiv:1605.00342.

21. Noncommutative homological mirror functor, with Cheol-Hyun Cho and Hansol Hong, arXiv:1512.07128.

20. Geometric transitions and SYZ mirror symmetry, with Atsushi Kanazawa, arXiv:1503.03829.

19. Localized mirror functor constructed from a Lagrangian torus, with Cheol-Hyun Cho and Hansol Hong, arXiv:1406.4597.

18. Lagrangian Floer potential of orbifold spheres, with Cheol-Hyun Cho, Hansol Hong and Sang-Hyun Kim, Advances in Mathematics 306 (2017), 344-426.

17. Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}, with Cheol-Hyun Cho and Hansol Hong, Journal of Differential Geometry 106 (2017), no. 1, 45-126.

16. Open Gromov-Witten invariants, mirror maps and Seidel representations for toric manifolds, with Kwokwai Chan, Naichung Conan Leung and Hsian-Hua Tseng, Duke Mathematical Journal 166 (2017), no. 8, 1405-1462.

15. Non-Kaehler SYZ mirror symmetry, with Li-Sheng Tseng and Shing-Tung Yau, Communications in Mathematical Physics 340 (2015), no.1, 145-170.

14. Modularity of open Gromov-Witten potentials of elliptic orbifolds, with Jie Zhou, Communications in Number Theory and Physics 9 (2015), no.2, 345-385.

13. Gross fibration, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds, with Kwokwai Chan, Cheol-Hyun Cho and Hsian-Hua Tseng, Journal of Differential Geometry 103 (2016), no.2, 207-288.

12. Gross-Siebert's slab functions and open GW invariants for toric Calabi-Yau manifolds,
Mathematical Research Letters 22 (2015), no.3, 881-898.

11. Genaralized SYZ and homological mirror symmetry, with Cheol-Hyun Cho,
Handbook for Mirror Symmetries of Calabi-Yau and Fano Manifolds.

  1. 10.Open Gromov-Witten invariants and SYZ under local conifold transitions,
    Journal of the London Mathematical Society (2) 90 (2014), no. 2, 413-435.

  2. 9.Toric, global, and generalized SYZ,
    International Congress of Chinese Mathematicians 2013.

  3. 8.Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds, with Kwokwai Chan, Cheol-Hyun Cho and Hsian-Hua Tseng, Communications in Mathematical Physics 328 (2014), no. 1, 83-130.

  4. 7.Enumerative meaning of mirror maps for toric Calabi-Yau manifolds, with Kwokwai Chan, Naichung Conan Leung and Hsian-Hua Tseng, Advances in Mathematics 244 (2013), 605-625.

  5. 6.Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces, with Kwokwai Chan, International Mathematics Research Notices (2014), no. 14, 3759-3789.

  6. 5.Open Gromov-Witten invariants on toric manifolds,
    Oberwolfach Reports 9 (2012), no.2, 1265-1267.

  7. 4.Mirror maps equal SYZ maps for toric Calabi-Yau surfaces, with Baosen Wu and Naichung Leung, Bulletin of the London Mathematical Society 44 (2012), no.2, 255-270.

  8. 3.A relation for Gromov-Witten invariants of local Calabi-Yau threefolds, with Baosen Wu and Naichung Leung, Mathematical Research Letters 18 (2011), pp. 943-956.

  9. 2.SYZ mirror symmetry for toric Calabi-Yau manifolds, with Kwokwai Chan and Naichung Leung,
    Journal of Differential Geometry 90 (2012), pp. 177-250.

  10. 1.Conformal geometry and special holonomy, with Naichung Leung,
    Recent Advances in Geometric Analysis 11 (2010), pp. 195-209.

Hobbies besides mathematics

Room 230, Department of Mathematics and Statistics,

Boston University

111 Cummington Mall, Boston, MA 02215

Email: 1lau1@math.bu.edu (remove the two 1’s)

In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.

Michael Atiyah

About me

Teaching

Chinese flute


Kung Fu Novels (金庸,古龍,黃易...)

I am currently an assistant professor in the Department of Mathematics at Boston University.

I am an organizer of the Geometry and Physics Seminar.  You are welcome to attend!

Notes of selected talks

I hope you will find these notes helpful.  Comments are welcome.

A short trip to tropical geometry
Talk to high school students, The Chinese University of Hong Kong, 2016.

SYZ, tiling and modularity
Simons Center, 2015.

Generalized SYZ and homological mirror symmetry
ICM Satellite Conference 2014, Taiwan.

Toric, global, and generalized SYZ
International Congress of Chinese Mathematicians 2013.

Open GW invariants and Seidel elements of toric manifolds
Simons Center, 2012.

SYZ mirror symmetry for toric CY manifolds
The Chinese University of Hong Kong, 2011.

My main research interest lies in complex algebraic geometry and symplectic geometry, and also their close relations with Physics. More specifically, I work on mirror symmetry.  I am developing a constructive theory which leads to interesting results on SYZ, open Gromov-Witten invariants, mirror maps, homological mirror symmetry and modular forms.

Research interest

Pieces of beauty

The above figure shows several beautiful tessellations of the plane.  Polygon countings in the figure have miraculous relations with periods of elliptic curves.  It comes from my joint work with Cheol-Hyun Cho and Hansol Hong.  In my joint work with Jie Zhou, we relate the countings with modular forms.

The above figure shows a hexagon tiling and some related graphs.  It appears in the study of SYZ mirror symmetry, and is related to Riemann theta functions, modular forms, Gromov-Witten theory, and general-type varieties.  It comes from my joint work with Atsushi Kanazawa.