Xiang Tang

Assistant Professor

Office: Cupples I, 112B
Phone: (314)9359488
Fax: (314)9356839
Email address: xtang@math.wustl.edu
Post:  Department of Mathematics
           Washington University
           1 brookings Dr.  
           St. Louis, MO, 63130        

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.

Research Interest: symplectic geometry, noncommutative geometry and mathematical physics.

 Publications:

  1. 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.
  2. Quantization and Morita Equivalence for Constant Dirac Structures on Tori (with A. Weinstein), Ann. Inst. Fourier, 54, 5 (2004).
  3. A Counter Example of Invariant Deformation Quantization, Travaux mathematiques. Fasc. XVI, 273-283, av. Math., XVI Univ. Luxemb., Luxembourg, 2005.
  4. 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.
  5. Deformation Quantization of Pseudo Symplectic(Poisson) Groupoids, Geom. Funct. Anal.16 (2006), no. 3, 731-766.
  6. A note on Q-algebra and quantization, Lett. Math. Phys. 75 (2006), no. 1, 49--61.
  7. Hopfish algebras (with A. Weinstein, and C. Zhu), Pacific J. Math. 231 (2007), no. 1, 193--216.
  8. An algebraic index theorem for orbifolds (with M. Pflaum, and H. Posthuma), Adv. Math. 210 (2007), no. 1, 83--121.
  9. 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.
  10. Rankin-Cohen brackets and formal quantization (with P. Bieliavsky, and Y. Yao), Adv. Math. 212 (2007), no. 1, 293--314.
  11. Hopfish structure and modules over irrational rotation algebras (with C. Blohmann and A.Weinstein), Noncommutative Geometry and Mathematical Physics, Contemporary Mathematics 2008, Volume: 462.
  12. Quantization and holomorphic anomaly (with A. Schwarz), J. High Energy Phys., 03 (2007).
  13. Gelfand-Fuchs cohomology of invariant formal vector fields (with I. Shapiro), Math. Res. Lett. 15 (2008), no. 1, 129--148. 
  14. Hopf algebroids and secondary characteristic classes (with J. Kaminker), to appear in J. Noncommut. Geom.
  15. 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.
  16. A universal deformation formula for Connes-Moscovici's Hopf algebra without any projective structure (with Y. Yao), to appear in J. Noncommut. Geom.
 Preprints:
  1. Noncommutative Poisson structures on Orbifolds (with G. Halbout), preprint: math.QA/0606436.
  2. Quantization of Poisson-Hopf stacks associated with group Lie bialgebras (with G. Halbout), preprint: math.QA/0703359.
  3. Orbifold cup products and ring structures on Hochschild cohomologies (with M. Pflaum, H. Posthuma, and H. Tseng), preprint: arxiv.0706.0027.
  4. Equivariant Lefschetz number of differential operators (with G. Felder), preprint: arxiv.0706.1021.
  5. Cyclic cocycles on deformation quantizations and higher index theorems (with M. Pflaum and H. Posthuma), preprint: arxiv. 0805.0108.
  6. Deformations of linear Poisson orbifolds (with G. Halbout and J. Oudom), preprint: arxiv.0807.0027.

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