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.
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.


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), J. Noncommut. Geom. 3 (2009), no. 1, 1--25.
  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), J. Noncommut. Geom. 3 (2009), no. 2, 151--179.
  17. Noncommutative Poisson structures on Orbifolds (with G. Halbout), to appear in Trans. A.M.S.
  18. Quantization of Poisson-Hopf stacks associated with group Lie bialgebras (with G. Halbout), to appear in Pacific J. Math.
  19. Equivariant Lefschetz number of differential operators (with G. Felder), to appear in Math. Z.
  20. On the algebraic index for riemannian étale groupoids (with M. Pflaum and H. Posthuma), to appear in Lett. Math. Phys.
  21. Cyclic cocycles on deformation quantizations and higher index theorems (with M. Pflaum and H. Posthuma), to appear in Adv. Math.

 Preprints:

  1. Orbifold cup products and ring structures on Hochschild cohomologies (with M. Pflaum, H. Posthuma, and H. Tseng), preprint: arxiv.0706.0027.
  2. Deformations of linear Poisson orbifolds (with G. Halbout and J. Oudom), preprint: arxiv.0807.0027.
  3. Dunkl operator and quantization of $\mathbb{Z}_2$-singularity (with G. Halbout), preprint: arxiv.0908.4301.
  4. Duality between gerbes on orbifolds and mackey machine (with H. Tseng), in preparation.
  5. A survey on Rankin-Cohen deformations (with R. Rochberg and Y. Yao), preprint: arxiv.0909.4364.