Xiang Tang

Associate 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.
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.

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 Energ y 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. On the algebraic index for riemannian etale groupoids (with M. Pflaum and H. Posthuma), Lett. Math. Phys. 90 (2009), no. 1-3, 287--310.
  18. Noncommutative Poisson structures on Orbifolds (with G. Halbout),  Trans. Amer. Math. Soc. 362 (2010), no. 5, 2249--2277..
  19. Quantization of Poisson-Hopf stacks associated with group Lie bialgebras (with G. Halbout), Pacific J. Math. 245 (2010), no. 1, 99--118.
  20. Equivariant Lefschetz number of differential operators (with G. Felder), Math. Z 266 (2010), no.2, 451-470. .
  21. Cyclic cocycles on deformation quantizations and higher index theorems (with M. Pflaum and H. Posthuma), Adv. Math. 223 (2010), no. 6, 1958--2021.
  22. 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
  23. Deformations of noncommutative  linear Poisson orbifolds (with G. Halbout and J. Oudom), Int. Math. Res. Not (2011), no. 1, 1-39. .
  24. A survey on Rankin-Cohen deformations (with R. Rochberg and Y. Yao), to appear in Noncommutative Geometry, Fields Institute Communications Series.
  25. Dunkl operator and quantization of $\mathbb{Z}_2$-singularity (with G. Halbout), to appear in J. Reine Angew. Math.
  26. The Picard group of  a noncommutative algebraic quantum torus (with Y. Berest, A. Ramadoss),  to appear in J. Noncommut. Geom.
  27. Hochschild  (co)homology of the Dunkl operator quantization of  $\mathbb{Z}_2$-singularity (with A. Ramadoss), to appear in Int. Math. Res. Not.
  28. Hopf cyclic cohomology and Hodge theory for proper actions (with Y. Yao, W. Zhang),  to appear in J. Noncommut. Geom.
  29. From double Lie groupoids to local Lie 2-groupoids (with R. Mehta), to appear in Bull. Braz. Math. Soc.

 Preprints:

  1. Duality between gerbes on orbifolds and mackey machine (with H. Tseng), preprint: arXiv:1004.1376.
  2. Geometry of orbit spaces of proper Lie groupoids (with M. Pflaum and H. Posthuma), preprint: arXiv:1101.0180.
  3. K-theory of Equivariant Quantization (with Y. Yao), preprint: arXiv:1112.3103
  4. The localized longitudinal index theorem for Lie groupoids and the van Est map (with M. Pflaum and H. Posthuma), preprint: arXiv:1112.4857