Preprints
1. Heat kernels of perturbed operators and index theory on G-proper manifolds , with P. Piazza and H. Posthuma and X. Tang [arXiv]2. K-theory and Lefschetz formula for locally symmetric spaces [arXiv]
3. Heat kernel, large-time behavior, and representation theory, with S. Shen and X. Tang [arXiv]
Publications
1. K-theory and the quantization commutes with reduction problem, with N. HigsonChin. Ann. Math. Ser. B 35 (2015), pp. 703-732.
2. Dirac operators on quasi-Hamiltonian G-spaces,
J. Geom. Phys 106 (2016), pp. 70-86. [arXiv]
3. An equivariant index for proper actions III: the invariant and discrete series indices, with P. Hochs Differential Geom. Appl 49 (2016), pp. 1-22.[arXiv]
4. An equivariant index for proper actions I, with P. Hochs
J. Funct. Anal 272 (2017), no.2, pp. 661-704. [arXiv]
5. A K-homological approach to the quantization commutes with reduction problem,
J. Geom. Phys 112 (2017), pp. 29-44. [arXiv]
6. On the Vergne conjecture, with P. Hochs
Archiv der Mathematik 108 (2017), no. 1, 99-112.[arXiv]
7. An equivariant index for proper actions II: properties and applications, with P. Hochs
J. Noncommut. Geom. 108 (2017), no. 1, 99-112. [arXiv]
8. Equivariant indices of Spin^c-Dirac operators for proper moment maps, with P. Hochs
Duke Math. J. 166 (2017), no. 6, 1125-1178.[arXiv]
9. Quantization of Hamiltonian loop group spaces, with Y.Loizides
Math. Ann 374 (2019), no. 1-2, 681-722 [arXiv]
10. A geometric formula for multiplicities of K-types of tempered representations, with P. Hochs and S. Yu
Trans. Amer. Math. Soc. 372 (2019), no. 12, 8553-8586 [arXiv]
11. Spinor modules for Hamiltonian loop group spaces, with Y.Loizides and E.Meinrenken
J. Symplectic Geom. 18 (2020), no. 3, 889-937 [arXiv]
12. Witten deformation for Hamiltonian loop group spaces, with Y. Loizides
J. Funct. Anal. 278 (2020), no. 9 [arXiv]
13. A geometric realisation of tempered representations restricted to maximal compact subgroups, with P. Hochs and S. Yu Math. Ann. 378 (2020), no. 1-2, 97-152 [arXiv]
14. Spinc-Dirac operators and geometric quantization of b-symplectic manifolds, with M. Braverman and Y. Loizides J. Symplectic Geom. 19 (2021), no. 1, 1–36 [arXiv]
15. A KK-theoretic perspective on deformed Dirac operators, with Y. Loizides and R. Rodsphon Adv. Math. 380 (2021) [arXiv]
16. Log symplectic manifolds and [Q,R]=0 , withY. Loizides and Y. Lin and R. Sjamaar Int. Math. Res. Not. 2022, no. 18, 14034–14066 [arXiv]
17. An index theorem for higher orbital integrals, with P. Hochs and X. Tang Math. Ann. 382 (2022), no. 1-2, 169–202 [arXiv]
18. Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids , with Y. Loizides and Y. Lin and R. Sjamaar Pure Appl. Math. Q. 19 (2023), no. 4, 2067–2131
19. Riemannian foliations and geometric quantization , with Y. Loizides and Y. Lin and R. Sjamaar J. Geom. Phys. 198 (2024), Paper No. 105133. [arXiv]
20. Cartan Motion Group and Orbital Integrals, with X. Tang AMS Proceedings Symp. Pure Math. 105
21. On the Connes-Kasparov Isomorphism, I. The Reduced C*-algebra of a Real Reductive Group and the K-theory of the Tempered Dual, with P. Clare and N. Higson and X. Tang Japanese Journal of Mathematics. 19 (2024), no. 1, 67–109. [arXiv]
22. On the Connes-Kasparov Isomorphism, II. The Vogan Classification of Essential Components in the Tempered Dual, with P. Clare and N. Higson Japanese Journal of Mathematics. 19 (2024), no. 1, 111–141. [arXiv]
23. Higher orbital integrals, rho numbers and index theory, with P. Piazza and H. Posthuma and X. Tang Math. Ann. 391 (2025), no. 3, 3687–3763. [arXiv]
24. Higher Orbital Integrals, Cyclic Cocycles and Noncommutative Geometry, with X. Tang Forum of Math, Sigma. 13 (2025), Paper No. e37 [arXiv]