Xiang Tang

Professor of Mathematics

Office: Cupples I, 118
Fax: (314)9356839
Email address: xtang@math.wustl.edu
Post:  Department of Mathematics and Statistics
           Washington University
           1 brookings Dr.  
           St. Louis, MO, 63130        

Teaching: (Fall 2024)

Math 5045 Algebraic Topology

Research Interest: noncommutative geometry, symplectic 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. (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),  Methods and Applications of Analysis, 24, (2017), no. 2, 321-332.
  45. Coarse groupoid cohomology and Chern-Connes character (with R. Willett, and Y. Yao), Scientia Sinica Mathematica, 47 (12), 1879-1890 (2017).
  46. Constant symplectic 2-groupoids (with R. Mehta), Lett. Math. Phys. 108 (2018), no. 5, 1203-1223.
  47. Symplectic structures on the integration of exact Courant algebroids (with R. Mehta), J. Geom. Phys. 127 (2018), 68-83.
  48. Roe $C^*$-algebra for groupoids and generalized Lichnerowicz vanishing theorem for foliated manifolds (with R. Willett, and Y. Yao), Math Z., 290 (2018), no. 3-4, 1309-1338.
  49. A new index theorem for monomial ideals by resolutions (with R. Douglas, M. Jabbari, and G. Yu), J. Funct. Anal. 275 (2018), no. 3, 735-760.
  50. Robust two-sample test of high-dimensional mean vectors under dependence (with W. Wang, and N. Lin), J. Multivariate Anal. 169 (2019), 312-329.
  51. Resolutions of proper Riemannian Lie groupoids (with H. Posthuma, and K. Wang), Int. Math. Res. Not. IMRN 2021, no. 2, 1249-1287.  
  52. A quantum Leray-Hirsch theorem for banded gerbes (with H. Tseng), J. of Differential Geometry, 119 (2021), no. 3, 459-511.
  53. An index theorem for quotients of Bergman spaces on egg domains (with M. Jabbari), Ann. K-Theory, 6 (2021), no. 2, 357–380.
  54. On gerbe duality and relative Gromov-Witten theory (with H. Tseng), Adv. Theor. Math. Phys. 25 (2021), no. 8, 2171-2177.
  55. An index theorem for higher orbital integrals (with P. Hochs, and Y. Song), Math. Ann. 382 (2022), no. 1-2, 169-202.
  56. On the Hochschild homology of convolution algebras of proper Lie groupoids (with M. Pflaum, and H. Posthuma), J. Noncommutat. Geom. 17 (2023), no.1, 101-162.
  57. Perturbations of pincipal submodules in the Drury-Arveson space (with M. Jabbari), J. Noncommutat. Geom. 17 (2023), no.1, 211-232.
  58. Cartan Motion Group and Orbital Integrals (with Y. Song), AMS Proceedings Symp. Pure Math. 105, American Mathematical Society, Providence, RI, (2023), 477-489.
  59. Primary and Secondary Invariants of Dirac Operators on G-proper Manifolds (with P. Piazza), AMS Proceedings Symp. Pure. Math. 105 American Mathematical Society, Providence, RI, (2023), 311-351.
  60. Trace Formula of Semicommutators (with Y. Wang, and D. Zheng), J. Funct. Anal., 285 (2023), no. 11, 110141.
  61. Helton-Howe Trace, Connes-Chern Character and Quantization (with Y. Wang, and D. Zheng), Adv. Math., 433 (2023), 109324.
  62. On the Connes-Kasparov Isomorphism, I. The Reduced C*-algebra of a Real Reductive Group and the K-theory of the Tempered Dual (with P. Clare, N. Higson, and Y. Song), Japanese J. Math. 19 (2024), 67-109.
  63. Higher Orbital Integrals, Cyclic Cocyles, and K-theory of Reduced Group $C^*$-algebra (with Y. Song), to appear in Forum of Mathematics, Sigma.
  64. Smooth Connes-Thom isomorphism, cyclic homology, and equivariant quantisation (with S. Chakraborty, and Y. Yao), to appear in Comm. Math. Phys.

Preprints:

  1. Higher orbital integrals, rho numbers and index theory (with P. Piazza, H. Posthuma, and Y. Song), arXiv:2108.0982.
  2. Mapping Cone and Morse Theory (with D. Clausen, and L. Tseng), arXiv:2211.11712.
  3. Heat kernels of perturbed operators and index theory on G-proper manifolds (with P. Piazza, H. Posthuma, and Y. Song), arXiv:2307.09252.
  4. Mapping Cone and Morse Theory (with D. Clausen and L. Tseng), arXiv:2405.2272.

Online Seminars (co-organized):

Professional Activities (recent):