Xin Jin

Research Interests

• Primary: Microlocal sheaves, symplectic topology, geometric representation theory, homological mirror symmetry, algebraic topology
• Secondary: Dynamical systems, especially chaotic billiards

My CV (PDF) | Research Statement (PDF)

Publications and Preprints

View full list on arXiv

1. Holomorphic Lagrangian branes correspond to perverse sheaves. Geom. Topol. 19 (2015), 1685–1735. [arXiv] [DOI]
2. Symplectomorphism group of T*(G/B) and the braid group I: A homotopy equivalence for G = SL_3(C). J. Symplectic Geom. 17 (2) (2019), 337–380. [arXiv] [DOI]
3. Representing the big tilting sheaves as holomorphic Morse branes. Adv. Math. 345 (2019), 845–860. [arXiv] [DOI]
4. Brane structures in microlocal sheaf theory. Joint with D. Treumann. J. Topology 17 (1) (2024), e12325, 68 pages. [arXiv] [DOI]
5. A Hamiltonian ∐_n BO(n)-action, stratified Morse theory and the J-homomorphism. Compositio Math. 160 (9), 2024, 2005--2099. [arXiv] [DOI]
6. Hyperbolicity of asymmetric lemon billiards. Joint with P. Zhang. Nonlinearity 34 (1) (2021), 92–117. [arXiv] [DOI]
7. Microlocal sheaf categories and the J-homomorphism. Submitted, 55 pages. [arXiv]
8. Birkhoff normal form and twist coefficients of periodic orbits of billiards. Joint with P. Zhang. Nonlinearity 35 (8) (2022), 3907–3943. [arXiv] [DOI]
9. Homoclinic and heteroclinic intersections for lemon billiards. Joint with P. Zhang. Adv. Math. 442 (2024), 109588, 67 pages. [arXiv] [DOI]
10. Homological mirror symmetry for the universal centralizers. 119 pages. [arXiv]
11. Cohomology of the universal centralizers I: the adjoint group case. 9 pages. [arXiv]
12. Mirror symmetry for the affine Toda systems. Joint with Z. Yun. 124 pages. [arXiv]
13. Multiplicative universal centralizers: cluster structure and mirror symmetry. Joint with B. Webster. In preparation.
14. Cohomology of the universal centralizers II: the semisimple group case. In preparation.