Preprints
1. Higher orbital integrals, rho numbers and index theory, with P. Piazza and H. Posthuma and X. Tang [arXiv]2. Heat kernel of perturbed operators and index theory on G-proper manifolds, with P. Piazza and H. Posthuma and X. Tang [arXiv]
3. Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids , with Y. Loizides and Y. Lin and R. Sjamaar
4. Riemannian foliations and geometric quantization , with Y. Loizides and Y. Lin and R. Sjamaar [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. IMRN. To appear [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. Cartan Motion Group and Orbital Integrals, with X. Tang AMS Proceedings Symp. Pure Math. To appear
19. Higher Orbital Integrals, Cyclic Cocycles and Noncommutative Geometry, with X. Tang Forum of Math, Sigma. To appear [arXiv]
20. 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. To appear [arXiv]
21. 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. To appear [arXiv]