Xiang Tang

Professor of Mathematics

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: (Fall 2017)

1. Math 203, Honors Mathematics

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


  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. (2009), no. 1, 1-25.
  15. A universal deformation formula for $\mathcal{H}_1$ without projectivity assumption (with Y. Yao), J. Noncommut. Geom. 3 (2009), no. 2, 151--179.
  16. On the algebraic index for riemannian \'etale groupoids (with M. Pflaum and H. Posthuma), Lett. Math. Phys. 90 (2009), no. 1-3, 287--310.
  17. Noncommutative Poisson structures on orbifolds (with G. Halbout),  Trans. Amer. Math. Soc. 362 (2010), no. 5, 2249--2277.
  18. Quantization of Poisson-Hopf stacks associated with group Lie bialgebras (with G. Halbout), Pacific J. Math. 245 (2010), no. 1, 99--118.
  19. Equivariant Lefschetz number of differential operators (with G. Felder), Math. Z. 266 (2010), no.2, 451-470.
  20. Cyclic cocycles on deformation quantizations and higher index theorems (with M. Pflaum and H. Posthuma), Adv. Math. 223 (2010), no. 6, 1958--2021.
  21. Asymptotic equivariant index of Toeplitz operators and relative index of CR structures (with L. Boutet de Monvel, E. Leichtnam, and A. Weinstein), Geometric aspects of analysis and mechanics, 57--79, Progr. Math., 292, Birkhause/Springer, New York, (2011).
  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 orbifolds with noncommutative  linear Poisson structures (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), Perspectives on noncommutative geometry, 133--151, Fields Inst. Commun., 61, Amer. Math. Soc., Providence, RI, (2011).
  25. From double Lie groupoids to local Lie 2-groupoids (with R. Mehta), Bull. Braz. Math. Soc. (N.S.), 42, (2011), no. 4, 651--681. 
  26. Hochschild  (co)homology of the Dunkl operator quantization of  $\mathbb{Z}_2$-singularity (with A. Ramadoss), Int. Math. Res. Not.  (2012), no. 9, 2123--2162.
  27. Quantization of Whitney functions (with M. Pflaum and H. Posthuma),  Travaus Mathematique, 20 (2012), 153--165.
  28. Dunkl operator and quantization of $\mathbb{Z}_2$-singularity (with G. Halbout), J. Reine Angew. Math.  673 (2012), 209--235. 
  29. The Picard group of  a noncommutative algebraic quantum torus (with Y. Berest, A. Ramadoss), J. Noncommut. Geom. 7 (2013), no. 2, 335--356.
  30. Hopf cyclic cohomology and Hodge theory for proper actions (with Y. Yao, W. Zhang), J. Noncommut. Geom. 7 (2013), no.3, 885--905.   
  31. Hochschild Lefschetz class for D-modules (with A. Ramadoss and H. Tseng), Math. Z. 275 (2013), no. 1-2, 367--388.
  32. Duality theorems of \'etale gerbes on orbifolds (with H. Tseng), Adv. Math. 250 (2014), 496--569.
  33. K-theory of equivariant quantization (with Y. Yao), J. Funct. Ana. 266 (2014), no. 2, 478-486.
  34. The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models (with L. Chen, T. Mazaheri, and A. Seidel), J. of Physics A: Math. and Theor. 47, (2014), 152001.
  35. Geometry of orbit spaces of proper Lie groupoids (with M. Pflaum and H. Posthuma), J. Reine Angew. Math. 694 (2014), 49-84. 
  36. Conjugacy classes and characters for extensions of finite groups (with H. Tseng), Chinese Annals of Mathematics, Series B, 35 (2014), no. 5, 743-750.
  37. The index of geometric operators on Lie groupoids (with M. Pflaum and H. Posthuma), Indag. Math (N.S.) 25 (2014), no.5, 1135-1153.
  38. Quantization of Whitney functions and reduction (with M. Pflaum and H. Posthuma), J. of Singul 13 (2015), 217-228.
  39. The transverse index theorem for proper cocompact actions of Lie groupoids (with M. Pflaum and H. Posthuma), J. of Differential Geometry, 99 (2015), no.3, 443-472.
  40. On the relative dual of an $S^1$-gerbe over an orbifold (with I. Shapiro and H. Tseng), Adv. Math. 270 (2015), 1-20.
  41. The localized longitudinal index theorem for Lie groupoids and the van Est map (with M. Pflaum and H. Posthuma), Adv. Math. 270 (2015), no.3, 223-262.
  42. An analytic Grothendieck Riemann Roch Theorem (with R. Douglas, and G. Yu), Adv. Math. 294 (2016), 307-331.
  43. Mechanices on fibered manifolds (with S. Li, and A. Stern), SIGMA, 13 (2017). 019.
  44. The Grauert--Grothendieck complex on differentiable spaces and a sheaf complex of Brylinski (with M. Pflaum, and H. Posthuma), to appear in Methods and Applications of Analysis.


  1. Symplectic structures on the integration of exact Courant algebroids (with R. Mehta), arXiv:1310.6587.
  2. A quantum Leray-Hirsch theorem for banded gerbes (with H. Tseng), arXiv:1602.03564.
  3. Roe $C^*$-algebra for groupoids and generalized Lichnerowicz Vanishing theorem for foliated manifolds (with R. Willett, and Y. Yao), arXiv:1605.07711.
  4. Constant symplectic 2-groupoids (with R. Mehta), arXiv:170201139.
  5. Resolutions of proper Riemannian Lie groupoids (with H. Posthuma, and K. Wang), arXiv:1706.07843.
  6. Coarse groupoid cohomology and Chern-Connes character (with R. Willett, and Y. Yao), preprint in Chinese.
  7. A new index theorem for monomial ideals by resolutions (with R. Douglas, M. Jabbari, and G. Yu), arXiv:1708.05796.