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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.
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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 Energy 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.
- Noncommutative Poisson
structures on Orbifolds (with G. Halbout), to appear in Trans. A.M.S.
- Quantization of Poisson-Hopf
stacks associated with group Lie bialgebras (with G. Halbout), to appear in Pacific J. Math.
- Equivariant Lefschetz number of
differential operators (with G. Felder), to appear in Math. Z.
- On the algebraic index for
riemannian étale groupoids (with M. Pflaum and H. Posthuma), to appear in Lett. Math. Phys.
- Cyclic cocycles on deformation
quantizations and higher index theorems (with M. Pflaum and H.
Posthuma), to appear in Adv. Math.
Preprints:
- Orbifold cup products and ring
structures on Hochschild cohomologies (with M. Pflaum, H. Posthuma, and
H. Tseng), preprint: arxiv.0706.0027.
- Deformations of linear Poisson
orbifolds (with G. Halbout and J. Oudom), preprint: arxiv.0807.0027.
- Dunkl operator and quantization
of $\mathbb{Z}_2$-singularity (with G. Halbout), preprint:
arxiv.0908.4301.
- Duality between gerbes on
orbifolds and mackey machine (with H. Tseng), in preparation.
- A survey on Rankin-Cohen
deformations (with R. Rochberg and Y. Yao), preprint: arxiv.0909.4364.
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