### 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. Higson

*Chin. 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**]