Xin Jin's Homepage

Research Interests:

• Primary: Microlocal sheaves, symplectic topology, geometric representation theory, homological mirror symmetry, algebraic topology, 

• Secondary: dynamical systems, especially chaotic billiards

My CV.

My Research Statement (updated 07/30/2024).

List of publications and preprints (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 \coprod_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. Homological mirror symmetry for the universal centralizers I: the adjoint group case. (Now part of item (11)). arXiv

9. Birkhoff normal form and twist coefficients of periodic orbits of billiards. Joint with P. Zhang. Nonlinearity 35 (8) (2022), 3907–3943. arXiv DOI

10. Homoclinic and heteroclinic intersections for lemon billiards. Joint with P. Zhang. Adv. Math. 442 (2024), 109588, 67 pages. arXiv DOI

11. Homological mirror symmetry for the universal centralizers. 119 pages. arXiv

12. Cohomology of the universal centralizers I: the adjoint group case. 9 pages. arXiv

13. Mirror symmetry for the affine Toda systems. Joint with Z. Yun. In preparation.

14. Multiplicative universal centralizers: cluster structure and mirror symmetry. Joint with B. Webster. In preparation.

15. Cohomology of the universal centralizers II: the semisimple group case. In preparation.