I was born in Guangzhou, China, and got my B.S. in Mathematics at Peking University , Beijing, China in 2006. In 2012, I accomplished my Ph.D. degree in Mathematics at the University of Minnesota under the supervision of Professor Tian-Jun Li.

My research interests lie in symplectic geometry and topology, including Floer theories, homological mirror symmetry, symplectomorphism groups, topology of Lagrangian submanifolds. Recently I also got interested in some problems in C1-generic dynamical systems.

• 16. Infinite connected components of the space of symplectic forms on ruled surfaces << Click me!
• Submitted, arXiv:2507.14636. (with Jianfeng Lin)
• We provide an infinite family of diffeomorphic symplectic forms on ruled surfaces, which are pairwise non-isotopic. This answers a uniqueness question regarding symplectic structures up to isotopy on closed symplectic four-manifolds.


• 15. Symplectic Torelli groups of rational surfaces
• Submitted, arXiv:2212.01873. (with Jun Li and Tian-Jun Li)
• In this work, we compute the symplectic mapping class group for all log Calabi–Yau surfaces except the E-types. Moreover, we show that the symplectic mapping class group is generated by Lagrangian spheres, answering a question of Donaldson in this class of symplectic four-manifolds.


• 14. Symplectic rational G-surfaces and equivariant symplectic cones
• J. Differ. Geom. , 119 (2), 221–260, October 2021. arXiv:1708.07500. Slides (IBS-Pohang)
• We give characterizations of finite groups \(G\) acting symplectically on rational surfaces (\(\mathbb{CP}^2\) blown up at two or more points). In particular, we obtain a symplectic version of the classical dichotomy between \(G\)-conic bundles and \(G\)-del Pezzo surfaces, analogous to a foundational result in algebraic geometry.


• 13. Symplectic −2 spheres and the symplectomorphism group of small rational 4-manifolds II
• Trans. Amer. Math. Soc. , 375 (2022), 1357–1410. arXiv:1911.11073. (with Jun Li and Tian-Jun Li)
• We study both the connected components and fundamental groups of symplectomorphism groups for small rational surfaces. In particular, for rational surfaces with Euler characteristic eight, we compute the symplectic mapping class group for all symplectic forms and relate it to braid groups on the sphere.


• 12. Spherical twists and Lagrangian spherical manifolds
• Selecta Math. (N.S.) , 25 (2019), 68. arXiv:1810.06533. (with Cheuk-Yu Mak)
• We study Dehn twists along Lagrangian submanifolds that are finite quotients of spheres. We describe the induced auto-equivalences on the derived Fukaya category and relate them to spherical functors. A new phenomenon is observed: these auto-equivalences decompose into spherical twists in characteristic zero, and yield entirely new auto-equivalences in non-zero characteristics.


• 11. Dehn twist exact sequences through Lagrangian cobordism
• Compositio Math. , 154(12), 2485–2533. arXiv:1509.08028. Slides (IAS). (with Cheuk-Yu Mak)
• We reinterpret various long exact sequences in symplectic topology as consequences of clean surgery and Biran–Cornea's Lagrangian cobordism theory—a "mirror" of Fourier–Mukai's construction of spherical/projective twists. We obtain a Floer-theoretic description of Lagrangian projective twists, confirming a mirror conjecture of Huybrechts–Thomas. Additionally, we introduce a "bottleneck formulation" for immersed Lagrangian cobordisms and a new algebraic technique to compute cobordism-induced connecting maps.


• 10. Gauged Floer homology and spectral invariants
• Int. Math. Res. Not. , 2018(13), 3959–4021. arXiv:1506.03349. (with Guangbo Xu)
• We establish spectral theory in gauged Floer homology, defining Entov–Polterovich-type quasi-morphisms and quasi-states. Applications include: (1) Proof of the weak Arnold conjecture for arbitrary toric manifolds without virtual techniques; (2) Extension of the theory of superheavy Lagrangians.


• 9. Equivariant split generation and mirror symmetry of special isogenous tori
• Adv. Math. , 323 (2018), 279–325. arXiv:1501.06257. Slides (CUHK).
• We prove homological mirror symmetry for "special isogenous tori," showing that the derived Fukaya category is a complete invariant in this class. Key innovations: (1) Generalization of Abouzaid's generation criterion to equivariant settings under free finite group actions; (2) Novel application of lattice quotient results from rigid analytic geometry.


• 8. Stability and existence of surfaces in symplectic 4-manifolds with b⁺=1
• J. Reine Angew. Math. (Crelle's Journal) , 2018(742), 115–155. arXiv:1407.1089. Slides (UMass). (with J. Dorfmeister and T.-J. Li)
• We completely classify the homology classes of smooth and symplectic (−4)-spheres in rational and ruled surfaces, and establish the existence of ADE-plumbings of Lagrangian spheres under minimal assumptions. Innovations include: (1) Extension of Opshtein–McDuff's non-generic Gromov–Witten technique to complex configurations; (2) Introduction of "tilted transport" for constructing symplectic submanifolds.


• 7. Symplectomorphism groups of non-compact manifolds, orbifold balls, and a space of Lagrangians
• J. Symp. Geom. , 14(1), 203–226. arXiv:1305.7291. (with R. Hind and M. Pinsonnault)
• We prove that the space of Lagrangian \(\mathbb{RP}^2\) in \(T^*\mathbb{RP}^2\) is contractible—a long-standing open problem. Our method gives a streamlined proof of Hind's result for \(S^2\), and reveals connections to: (1) Homotopy types of symplectomorphism groups for non-compact manifolds with concave ends; (2) Spaces of orbifold embeddings.


• 6. The symplectic mapping class group of CP²#nCP², n≤4
• Michigan Math. J. , 64 (2015), 319–333. arXiv:1310.7329. (with J. Li and T.-J. Li)
• We establish the connectedness of symplectomorphism groups for small rational surfaces, resolving fundamental structural questions in low-dimensional symplectic topology.


• 5. On an exotic Lagrangian torus in CP²
• Compositio Math. , 151 (2015), 1372–1394. arXiv:1201.2446.
• By studying a semi-toric system with an RP²-singularity, we discover a superheavy fiber via Fukaya–Oh–Ohta–Ono's framework, negatively answering Entov–Polterovich's question on whether RP² is a stem in CP². Key innovation: A new method for counting holomorphic disks with Lagrangian boundaries in singular toric systems.


• 4. Exact Lagrangians in A_n-singularities
• Math. Ann. , 359 (2014), no. 1–2, 153–168. arXiv:1302.1598.
• We resolve two long-standing open problems: (1) Isotopy classification of compactly supported symplectomorphisms; (2) Isotopy classification of Lagrangian spheres in \(A_n\)-surface Milnor fibers. The core innovation is the construction of ball-swapping symplectomorphisms as symplectic analogues of algebraic monodromy maps.


• 3. Spherical Lagrangians via ball packings and symplectic cutting
• Selecta Math. (N.S.) , 20 (2014), no. 1, 261–283. arXiv:1211.5952. (with M. S. Borman and T.-J. Li)
• We resolve open questions on the uniqueness of Lagrangian submanifolds: (1) Smooth and symplectic uniqueness of Lagrangian \(S^2\) and \(\mathbb{RP}^2\) embeddings in 4-dimensional rational and ruled manifolds; (2) Construction of smoothly knotted \(\mathbb{RP}^2\) embeddings under varying symplectic forms.


• 2. Lagrangian spheres, symplectic surfaces and symplectic mapping class groups
• Geom. & Topol. , 16 (2012), 1121–1169. arXiv:1012.4146. (with T.-J. Li)
• Key advances on Lagrangian spheres: (1) Complete homology classification of \(S^2\) embeddings in rational and ruled surfaces; (2) Factorization of symplectomorphism actions via Lagrangian Dehn twists; (3) Hamiltonian uniqueness for \(S^2\) in rational surfaces with \(\chi < 8\); (4) New proofs for Lagrangian embeddings in \(S^2 \times S^2\) and \(\mathbb{CP}^2\).


• 1. Note on a theorem of Bangert
• Acta Math. Sin. (Engl. Ser.) , 28 (2012), no. 1, 121–132. arXiv:1509.08128. (with T.-J. Li)
• A preliminary study of uniruledness in complete non-compact symplectic manifolds with non-cylindrical almost complex structures. The main result establishes non-hyperbolicity for asymptotically standard symplectic manifolds.

• Detecting Non-displaceable fibers in toric degenerations , preliminary version.
  This paper is subsumed by "Spherical Lagrangians via ball packings and symplectic cutting". However, it still contains some preliminary results that is not contained in the aforementioned paper.
  
  
• Slides for a talk in CIRGET (joint Geometry seminar in Montreal city), summarizing some main results of my work in symplectic 4-manifolds (2, 3, 4, 6, 8 in the publication list), with emphasis on the relations to symplectic packing problems.

American Mathematical Society,
MathSciNet
Zoom reading seminar for 2020 summer