*This page will no longer be updated starting from 01/16/2018. Jump to here for my most up-to-date information on research.*

13. *Symplectic rational G-surfaces and equivariant symplectic cones. ***Submitted, ***arXiv:1708.07500. *(with Weimin Chen, Tian-Jun Li)

We give characterizations of a finite group G acting symplectically on a rational surface (\CP^2 blown up at two or more points). In particular, we obtain a symplectic version of the dichotomy of G-conic bundles versus G-del Pezzo surfaces for the corresponding G-rational surfaces, analogous to a classical result in algebraic geometry.

Besides the characterizations of the group G (which is completely determined for the case of \CP^2#N\overline\CP^2, N=2,3,4), we also investigate the equivariant symplectic minimality and equivariant symplectic cone of a given G-rational surface.

12. *Symplectic −2 spheres and the symplectomorphism group of small rational 4-manifolds. arXiv:1611.07436. *(with Jun Li, Tian-Jun Li)

We study both connected components and fundamental groups of the symplectomorphism groups for small rational surfaces. Especially, when the rational surface has Euler characteristic eight, we computed the symplectic mapping class groups for all symplectic forms, and related them to braid groups on a sphere.

11. *Dehn twists exact sequences through Lagrangian cobordism.** *** Submitted*** , arXiv:1509.08028. *(with Cheuk-Yu Mak)

We give a new point of view to various long exact sequences in the symplectic literature. In particular, we interpret them as a direct consequence of a clean surgery construction and Biran-Cornea's Lagrangian cobordism theory. This is a "mirror" construction of the Fourier-Mukai construction of spherical/projective twists in algebraic geometry. We also obtained a Floer-theoretic description of Lagrangian projective twists, confirming a mirror conjecture of Huybrechts and Thomas.

10. *Gauged Floer homology and spectral invariants*. * ***IMRN**, to appear arXiv:1506.03349. (with Guangbo Xu)

9. *Equivariant split generation and mirror symmetry of special isogenous tori. ***Advances in Mathematics*** , *to appear,

**arXiv:1501.06257.**
8. *Stability and existence of surfaces in symplectic 4-manifolds with b+=1*. **J. Reine Angew. Math. (Crelle's Journal), **to appear, arXiv:1407.1089. (with J. Dorfmeister and T.-J. Li.)

We completely classified the homology class of smooth and symplectic (-4)-spheres in rational and ruled surfaces, and established the existence of ADE-plumbing of Lagrangian spheres under minimal assumption. Two main technical innovations were made: we extended part of Opshtein-Mcduff's non-generic Gromov-Witten technique to more complicated non-generic configurations, and we introduced a "tilted transport" to construct symplectic submanifolds.

7. * Symplectormophism groups of non-compact manifolds, orbifold balls, and a space of Lagrangians*. **J. Symp. Geom.**, to appear, arXiv 1305.7291. (with R. Hind and M. Pinsonnault)

6. *The symplectic mapping class group of $\CP^2\#n\overline{\CP^2}$, \leq 4$*. **Michigan Math. J.**, 64 (2015), 319-333. Journal link. arXiv:1310.7329. (with J. Li and T.-J. Li)

5. * On an exotic Lagrangian torus in $\CP^2$*. **Compositio Math. ** 151 (2015), 1372-1394, Journal link. arXiv 1201.2446.

4. *Exact Lagrangians in A_n-singularities*. **Math. Ann.**, 359 (2014), no. 1-2, 153-168. Journal link, arXiv 1302.1598.

3. * Spherical Lagrangians via ball packings and symplectic cutting*. **Selecta Math. (N.S.)**, 20 (2014), no. 1, 261-283. Journal Link, arXiv 1211.5952. (with M. S. Borman and T.-J. Li)

2. * Lagrangian spheres, symplectic surfaces and symplectic mapping class groups*. **Geom. & Topo. **16 (2012), 1121-1169. Journal Link, arXiv 1012.4146. (with T.-J. Li)

▸ We classified completely the homology class of Lagrangian $S^2$ embeddings into rational or ruled surfaces.

▸ We factorized the homological action of any symplectomorphism of rational or ruled surfaces into composition of Lagrangian Dehn twists.

▸ New short proof to Lagrangian embeddings of $S^2$ into $S^2\times S^2$ and $\RP^2$ into $\CP^2$ and $T^*\RP^2$.

▸ Hamiltonian uniqueness of $S^2$ in rational surfaces with Euler number less than 8.

1. * Note on a theorem of Bangert. ***Acta Math. Sin. (Engl. Ser.)** 28 (2012), no. 1, 121-132. Journal Link, arXiv:1509.08128. (with T.-J. Li)

**non-cylindrical**almost complex structure. We establish the non-hyperbolicity property of almost complex structures on an asymptotically standard symplectic manifold.

**Work In Progress:**

- Dehn twists along Lagrangian spherical space forms. (with C.Y. Mak)
- Finite symplectic symmetries and orbifold cohomology. (with L. Amorim, S.C. Lau)
- Donaldson hypersurfaces in orbifold theory. (with G. Xu)