Research
I am interested in equivariant index theory for manifolds with various group actions, and interactions with non-commutative geometry, symplectic geometry and representation theory.

Preprints

1. A geometric realisation of tempered representations restricted to maximal compact subgroups, with P. Hochs and S. Yu [arXiv

2. A KK-theoretic perspective on deformed Dirac operators, with Y. Loizides and and R. Rodsphon [arXiv

3. Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra, with X. Tang [arXiv

4. Spinc-Dirac operators and geometric quantization of b-symplectic manifolds, with M. Braverman and Y. Loizides [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. To appear [arXiv

11. Spinor modules for Hamiltonian loop group spaces, with Y.Loizides and E.Meinrenken
J. Symplectic Geom. To appear [arXiv

12. Witten deformation for Hamiltonian loop group spaces, with Y. Loizides
J. Funct. Anal. To appear [arXiv