Research
Interest:
noncommutative
geometry, symplectic geometry, and mathematical
physics.
Publications:
 Thermodynamics
of the general diffusion process:
timereversibility and entropy production
(with H. Qian & M. Qian),Journal of
Statistical Physics, Vol. 107, Nos. 5/6, June
(2002).
 Quantization
and Morita equivalence for constant Dirac
structures on tori (with A. Weinstein), Ann.
Inst. Fourier, 54, 5 (2004).
 A counter
example of invariant deformation quantization,
Travaux mathematiques. Fasc. XVI, 273283, av.
Math., XVI Univ. Luxemb., Luxembourg, (2005).
 Homology
of formal deformations of proper etale Lie
groupoids (with N. Neumaier, M. Pflaum, and H.
Posthum), J. Reine Angew. Math. 593 (2006),
117168.
 Deformation
Quantization of Pseudo Symplectic(Poisson)
Groupoids, Geom. Funct. Anal.16 (2006),
no. 3, 731766.
 A note
on Qalgebra and quantization, Lett. Math.
Phys. 75 (2006), no. 1, 4961.
 Hopfish
algebras (with A. Weinstein, and C. Zhu), Pacific
J. Math. 231 (2007), no. 1, 193216.
 An
algebraic index theorem for orbifolds (with M.
Pflaum, and H. Posthuma), Adv. Math. 210 (2007),
no. 1, 83121.
 Poisson
geometry and deformation quantization near a
pseudoconvex boundary (with E. Leichtnam, and
A. Weinstein), J. Eur. Math. Soc. (JEMS) 9
(2007), no. 4, 681704.
 RankinCohen
brackets and formal quantization (with P.
Bieliavsky, and Y. Yao), Adv. Math. 212 (2007),
no. 1, 293314.
 Hopfish
structure and modules over irrational rotation
algebras (with C. Blohmann and A.Weinstein), Noncommutative
Geometry and Mathematical Physics, Contemporary
Mathematics 2008, Volume: 462.
 Quantization
and holomorphic anomaly (with A. Schwarz), J.
High Energy Phys., 03 (2007).
 GelfandFuchs
cohomology of invariant formal vector fields
(with I. Shapiro), Math. Res. Lett. 15 (2008),
no. 1, 129148.
 Hopf
algebroids and secondary characteristic classes
(with J. Kaminker), J. Noncommut. Geom. (2009),
no. 1, 125.
 A universal
deformation formula for $\mathcal{H}_1$ without
projectivity assumption (with Y. Yao), J.
Noncommut. Geom. 3 (2009), no. 2, 151179.
 On the
algebraic index for riemannian \'etale groupoids
(with M. Pflaum and H. Posthuma), Lett. Math.
Phys. 90 (2009), no. 13, 287310.
 Noncommutative
Poisson structures on orbifolds (with G.
Halbout), Trans. Amer. Math. Soc. 362
(2010), no. 5, 22492277.
 Quantization
of PoissonHopf stacks associated with group Lie
bialgebras (with G. Halbout), Pacific J.
Math. 245 (2010), no. 1, 99118.
 Equivariant
Lefschetz number of differential operators
(with G. Felder), Math. Z. 266 (2010), no.2,
451470.
 Cyclic
cocycles on deformation quantizations and higher
index theorems (with M. Pflaum and H.
Posthuma), Adv. Math. 223 (2010), no. 6,
19582021.
 Asymptotic
equivariant index of Toeplitz operators and
relative index of CR structures (with L.
Boutet de Monvel, E. Leichtnam, and A. Weinstein),
Geometric aspects of analysis and mechanics,
5779, Progr. Math., 292, Birkhause/Springer, New
York, (2011).
 Orbifold cup
products and ring structures on Hochschild
cohomologies (with M. Pflaum, H. Posthuma, and
H. Tseng), Comm. Comtemp. Math. 13 (2011), no.
13, 123182.
 Deformations
of orbifolds with noncommutative linear
Poisson structures (with G. Halbout and J.
Oudom), Int. Math. Res. Not. (2011), no. 1,
139.
 A survey on
RankinCohen deformations (with R. Rochberg
and Y. Yao), Perspectives on noncommutative
geometry, 133151, Fields Inst. Commun., 61,
Amer. Math. Soc., Providence, RI, (2011).
 From double
Lie groupoids to local Lie 2groupoids (with
R. Mehta), Bull. Braz. Math. Soc. (N.S.), 42,
(2011), no. 4, 651681.
 Hochschild
(co)homology
of the Dunkl operator quantization of
$\mathbb{Z}_2$singularity (with A. Ramadoss),
Int. Math. Res. Not. (2012),
no. 9, 21232162.
 Quantization
of Whitney functions (with M. Pflaum and H.
Posthuma), Travaus Mathematique, 20
(2012), 153165.
 Dunkl
operator and quantization of
$\mathbb{Z}_2$singularity (with G. Halbout),
J. Reine Angew. Math. 673 (2012),
209235.
 The Picard
group of a noncommutative algebraic quantum
torus (with Y. Berest, A. Ramadoss), J.
Noncommut. Geom. 7 (2013), no. 2, 335356.
 Hopf cyclic
cohomology and Hodge theory for proper actions
(with Y. Yao, W. Zhang), J. Noncommut. Geom. 7
(2013), no.3, 885905.
 Hochschild
Lefschetz class for Dmodules (with A.
Ramadoss and H. Tseng), Math. Z. 275 (2013), no.
12, 367388.
 Duality
theorems of \'etale gerbes on orbifolds (with
H. Tseng), Adv. Math. 250 (2014), 496569.
 Ktheory
of equivariant quantization (with Y. Yao), J.
Funct. Ana. 266 (2014), no. 2, 478486.
 The
impossibility of exactly flat nontrivial Chern
bands in strictly local periodic tight binding
models (with L. Chen, T. Mazaheri, and A.
Seidel), J. of Physics A: Math. and Theor. 47,
(2014), 152001.
 Geometry of
orbit spaces of proper Lie groupoids (with M.
Pflaum and H. Posthuma), J. Reine Angew. Math.
694 (2014), 4984.
 Conjugacy
classes and characters for extensions of finite
groups (with H. Tseng), Chinese
Annals of Mathematics, Series B, 35 (2014),
no. 5, 743750.
 The index of
geometric operators on Lie groupoids (with M.
Pflaum and H. Posthuma), Indag. Math (N.S.) 25
(2014), no.5, 11351153.
 Quantization
of Whitney functions and reduction (with M.
Pflaum and H. Posthuma), J. of Singul 13 (2015),
217228.
 The
transverse index theorem for proper cocompact
actions of Lie groupoids (with M. Pflaum and
H. Posthuma), J. of Differential Geometry, 99
(2015), no.3, 443472.
 On the
relative dual of an $S^1$gerbe over an orbifold
(with I. Shapiro and H. Tseng), Adv. Math. 270
(2015), 120.
 The
localized longitudinal index theorem for Lie
groupoids and the van Est map (with M. Pflaum
and H. Posthuma), Adv. Math. 270 (2015), no.3,
223262.
 An analytic
Grothendieck Riemann Roch Theorem (with R.
Douglas, and G. Yu), Adv. Math. 294 (2016),
307331.
Preprints:
 Symplectic structures
on the integration of exact Courant algebroids (with
R. Mehta), preprint: arXiv:1310.6587.
 Mechanices on fibered
manifolds (with S. Li, and A. Stern), preprint:
arXiv:1511.00061.
 A quantum LerayHirsch
theorem for banded gerbes (with H. Tseng), preprint:
arXiv:1602.03564.
 The
GrauertGrothendieck complex on differentiable
spaces and a sheaf complex of Brylinski (with M.
Pflaum, and H. Posthuma),
preprint: arXiv:1605.06105.
 Roe $C^*$algebra for
groupoids and generalized Lichnerowicz
Vanishing theorem for foliated manifolds (with
R. Willett, and Y. Yao), preprint: arXiv:1605.07711.
