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Teaching:
1. 2006, Math
217, Differential equations, Section 01: 9-10,
Section 02: 11-12 Fall.
2. 2008, Math 217, Differential equations, Section
01:10-11, Spring.
3. 2008, Math 563, Topics in Lie Groups and
Algebras I:
Introduction to Lie algebras and Lie groups,
Spring.
4. 2008, Math 417, An introduction to topology and
modern analysis,
Fall.
5. 2009, Math 309, Matrix algebra, Spring.
6. 2009, Math 418, An introduction to topology and
modern analysis,
Spring.
7. 2009, Math 429,
Linear algebra, Fall.
8. 2009, Math 217, Differential equations, Section
01:9-10, Fall.
9. 2010, Math
430, Modern algebra, Spring.
10. 2010, Math 309, Matrix algebra, Fall.
11. 2011,
Math 217, Differential equation, Spring.
12. 2012, Math
308, Mathematics for Physical Sciences, Spring.
13. 2012, Math
430, Modern algebra, Spring.
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Research
Interest:
symplectic
geometry,
noncommutative geometry and mathematical physics.
Publications:
- Thermodynamics
of the
General
Diffusion Process: Time-Reversibility 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,
273-283, 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),
117-168.
- Deformation
Quantization of
Pseudo Symplectic(Poisson) Groupoids, Geom.
Funct. Anal.16
(2006),
no. 3, 731-766.
- A note
on Q-algebra and
quantization, Lett. Math. Phys. 75 (2006),
no. 1, 49--61.
- Hopfish
algebras (with A.
Weinstein, and C. Zhu), Pacific J. Math. 231
(2007), no. 1,
193--216.
- An
algebraic index theorem
for
orbifolds (with M. Pflaum, and H. Posthuma), Adv.
Math. 210
(2007),
no. 1, 83--121.
- Poisson
geometry and
deformation
quantization near a pseudoconvex boundary
(with E. Leichtnam, and
A.
Weinstein), J. Eur. Math. Soc. (JEMS) 9 (2007),
no. 4, 681--704.
- Rankin-Cohen
brackets and
formal
quantization (with P. Bieliavsky, and Y. Yao),
Adv. Math. 212
(2007), no. 1, 293--314.
- 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 Energ y
Phys., 03 (2007).
- Gelfand-Fuchs
cohomology of
invariant formal vector fields (with I.
Shapiro), Math. Res.
Lett.
15 (2008), no. 1, 129--148.
- Hopf
algebroids and secondary
characteristic classes (with J. Kaminker), J. Noncommut. Geom.
3
(2009), no. 1, 1--25.
- Asymptotic
equivariant index of
Toeplitz operators and relative index of CR
structures (with L.
Boutet
de Monvel, E. Leichtnam, and A. Weinstein), to
appear in the
Proceeding for Hans Duistermaat's 65th birthday.
- A universal
deformation formula
for Connes-Moscovici's Hopf algebra without any
projective structure
(with Y. Yao), J. Noncommut.
Geom. 3 (2009), no. 2, 151--179.
- On the
algebraic index for
riemannian etale groupoids (with M. Pflaum and
H. Posthuma), Lett.
Math. Phys. 90 (2009), no. 1-3, 287--310.
- Noncommutative
Poisson
structures on Orbifolds (with G.
Halbout), Trans. Amer.
Math. Soc. 362 (2010), no. 5, 2249--2277..
- Quantization
of Poisson-Hopf
stacks associated with group Lie bialgebras
(with G. Halbout), Pacific
J. Math. 245 (2010), no. 1, 99--118.
- Equivariant
Lefschetz number of
differential operators (with G. Felder), Math. Z
266 (2010), no.2, 451-470. .
- Cyclic
cocycles on deformation
quantizations and higher index theorems (with
M. Pflaum and H.
Posthuma), Adv. Math. 223 (2010), no. 6,
1958--2021.
- Orbifold cup
products and ring
structures on Hochschild cohomologies (with M.
Pflaum, H. Posthuma,
and
H. Tseng), Comm. Comtemp. Math. 13 (2011),
no. 13, 123-182
- Deformations
of
noncommutative linear Poisson
orbifolds (with G. Halbout and J. Oudom), Int.
Math.
Res. Not (2011), no. 1, 1-39.
.
- A
survey on
Rankin-Cohen
deformations (with R. Rochberg and Y. Yao), to appear in
Noncommutative Geometry,
Fields Institute Communications Series.
- Dunkl
operator and
quantization
of $\mathbb{Z}_2$-singularity (with G.
Halbout), to appear in
J. Reine Angew. Math.
- The
Picard group
of a noncommutative algebraic quantum torus
(with Y. Berest,
A. Ramadoss), to appear in J. Noncommut.
Geom.
- Hochschild
(co)homology
of the Dunkl operator quantization of
$\mathbb{Z}_2$-singularity (with A. Ramadoss),
to appear in Int.
Math. Res. Not.
- Hopf
cyclic cohomology and Hodge theory for proper
actions
(with Y. Yao, W. Zhang), to appear in
J. Noncommut. Geom.
- From
double Lie groupoids to
local Lie 2-groupoids (with R. Mehta), to
appear in Bull. Braz. Math. Soc.
Preprints:
- Duality between
gerbes on
orbifolds and mackey machine (with H. Tseng),
preprint:
arXiv:1004.1376.
- Geometry of orbit
spaces of
proper Lie groupoids (with M. Pflaum and H.
Posthuma),
preprint: arXiv:1101.0180.
- K-theory of
Equivariant Quantization (with Y. Yao), preprint:
arXiv:1112.3103
- The localized
longitudinal index theorem for Lie groupoids and
the van Est map (with M. Pflaum and H. Posthuma),
preprint: arXiv:1112.4857
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