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Research
My research interest is symplectic and contact topology. Roughly speaking, symplectic geometry is the geometry of generalized phase spaces in Hamiltonian mechanics, encoding both the position and the momentum of the objects. The word 'symplectic' is made up by H. Weyl by translating 'complex' into Greek.
More specifically, my research interest is in algebraic and categorical invariants in symplectic and contact topology coming from microlocal sheaf theory, pseudo-holomorphic curves and generating families, with their connections to cluster algebras, mirror symmetry, noncommutative geometry, geometric representation theory, algebraic K-theory and persistence modules. I am also interested in the flexibility side of symplectic and contact topology involving h-principles.
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Papers and Preprints
- 17. Degeneration as localization for wrapped Fukaya categories, joint with Sheel Ganatra, Si-Yang Liu and Peng Zhou, in preparation.
- 16. A remark on integral transforms of wrapped sheaves, joint with Christopher Kuo, Sheel Ganatra and Haosen Wu, in preparation.
- 15. Capacities from the Chiu-Tamarkin complexes II, joint with Bingyu Zhang, in preparation.
- 14. Cyclic homology of sheaf categories, joint with Bingyu Zhang, in preparation.
- 13. Microsheaf composition of Lagrangian correspondences, joint with David Nadler and Vivek Shende, 105pp, arXiv.
- 12. C^0-rigidity of Legendrians and coisotropics via sheaf quantization, joint with Tomohiro Asano, Yuichi Ike and Christopher Kuo, 45pp, arXiv.
- 11. Decompositions of augmentation varieties via weaves and rulings, joint with Johan Asplund, Orsola Capovilla-Searle, James Hughes, Caitlin Leverson and Angela Wu, 88pp, arXiv.
- 10. Positive microlocal holonomies are globally regular, joint with Roger Casals, 34pp, Comm. Amer. Math Soc. 6 (2026), 492-535, journal, arXiv.
- 9. Relative Calabi-Yau structure on microlocalization, joint with Christopher Kuo, 50pp, arXiv.
- 8. Duality and kernels in microlocal geometry, joint with Christopher Kuo, Int. Math. Res. Not. 2025, no.6, 1-34, journal, arXiv.
- 7. Lagrangian cobordism and shadow distance in Tamarkin category, joint with Tomohiro Asano and Yuichi Ike, Sel. Math. New Ser. 31, 45 (2025), journal, arXiv.
- 6. Existence of generating families on Lagrangian cobordisms, Math. Ann. 390, (2024): 5471–5494, journal, arXiv.
- 5. Lagrangian cobordism functor in microlocal sheaf theory II, J. Sympl. Geom. 23 no.3 (2025): 599-672, journal, arXiv.
- 4. Spherical adjunction and Serre functor from microlocalization, joint with Christopher Kuo, 62pp, arXiv.
- 3. Conjugate fillings and Legendrian weaves, joint with Roger Casals, 100pp, arXiv.
- 2. Lagrangian cobordism functor in microlocal sheaf theory I, J. Topol. 16.3 (2023): 1113-1166, journal, arXiv.
- 1. Estimating Reeb chords using microlocal sheaf theory, 39pp, to appear in Algebr. Geom. Topol., journal, arXiv.
Research Notes
- 2. Sheaf quantization of geometrically bounded exact Lagrangians, pdf. The mathematical content is essentially extracted from Lagrangian cobordism functor in microlocal sheaf theory II Section 3.3 and my thesis Some functoriality results for microlocal sheaves over Legendrians and Lagrangians Section 4.2-4.3.
- 1. Functoriality of sheaf categories over Weinstein manifolds, pdf. The mathematical content is essentially extracted from Lagrangian cobordism functor in microlocal sheaf theory I Section 3.2.
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