Publications :

A mod 2 index theorem for pin^- manifolds. Science China Mathematics 60 (2017), 1615–1632.

(with F. Han and K. Liu) Anomaly cancellation and modularity, II: the E8 × E8 case. Science China Mathematics 60 (2017), 985-994.

(with J.-M. Bismut and X. Ma) Asymptotic torsion and Toeplitz operators. Journal of the Institute of Mathematics of Jussieu 16 (2017), 223-349.

Positive scalar curvature on foliations. Annals of Mathematics 185 (2017), 1035-1068.

Positive scalar curvature on foliations (a talk)

Analytic localization and Riemann-Roch (a talk)

$\eta$-invariants and the Poincare-Hopf index formula. Geometry and Topology of Submanifolds X, pp. 336-345. World Scientific, Singapore, 2000.

(with F. Han and K. Liu) Anomaly cancellation and modularity. in Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics. (2014)

(With X. Ma) Eta-invariant and flat vector bundles II. in Inspired by S. S. Chern. Ed. P. A. Griffiths, Nankai Tracts in Mathematics Vol. 11. World Scientific, 2006, pp. 335-350.

局部指标理论简介 （中科院数学所讲座）

The Mathematical Work of V. K. Patodi. Commun. Math. Stat. (2014), 253–277.

(with F. Han) η-Invariant and modular forms. The Quarterly Journal of Mathematics 66 (2015), 133–142.

(with X. Dai) Eta invariant and holonomy: The even dimensional case. Adv. in Math. 279 (2015), 291-306.

(with K. Liu) Adiabatic limits and foliations. Contemp. Math. 279 (2001), 195-208.

(with X. Ma) Transversal index and L^2-index for manifolds with boundary.

(with X. Ma) Geometric quantization for proper moment maps: the Vergne conjecture. Acta Mathematica 212 (2014), 11-57.

(with Z. Tang) η-Invariant and a problem of Bérard-Bergery on the existence of closed geodesics. Advances in Mathematics 254 (2014), 41-48.

(with X. Tang and Y. Yao) Hopf cyclic cohomology and Hodge theory for proper actions. Journal of Noncommutative Geometry 7 (2013), 885-905.

Eta invariant and closed geodesics ( a talk)

Spin^c-manifolds and Rokhlin congruences. C. R. Acad. Sci. Paris, Serie I, 317 (1993), 689-692

(with F. Han and K. Liu), Modular forms and generalized anomaly cancellation formulas. J. Geom. Phys. 62 (2012), 1038-1053.

A mod 2 index theorem for pin^- manifolds. Preprint, MSRI 053-94.

(with J.-M.Bismut and X. Ma), Opérateurs de Toeplitz et torsion analytique asymptotique. C. R. Acad. Sci. Paris, Serie I. 349 (2011), 977-981.

(with Q. Chen and F. Han) Generalized Witten genus and vanishing theorems. J. Diff. Geom. 88 (2011), 1-39.

(with H. Feng and W. Li) A Poincare-Hopf type formula for Chern character numbers. Math. Z. 269 (2011), 401-410..

(with X. Dai) Adiabatic limit, Bismut-Freed connection, and the real analytic torsion form. J. reine angew. Math. 647 (2010), 87–113.

(with V. Mathai) Geometric quantization for proper actions (with an Appendix by U. Bunke) 225 (2010), 1224-1247.

(with Q. Chen and F. Han) Witten genus and vanishing results on complete intersections. C. R. Math. Acad. Sci. Paris, Ser. I 348 (2010), 295-298

Geometric quantization on manifolds with boundary (a conference talk at Okinawa, 2010.1.29)

Cobordism and Rokhlin congruences. Acta Math. Scientia 29B (2009), 609-612.

(with X. Ma) Geometric quantization for proper moment maps. C. R. Math. Acad. Sci. Paris, Ser. I 347 (2009), 389-394.

(with Huitao Feng and Guangbo Xu) Real embeddings, eta invariant and Chern-Simons current. Pure and Applied Mathematics Quarterly 5 (2009), 1113-1137.

(with X. Ma) Bergman kernels and symplectic reduction. Asterisque, Tom. 318, Soc. Math. France, pp. 1-154, 2008.

Analytic aspects of index theory (My Habilitation thesis), 2008.

(with Guangxiang Su) A Cheeger-Mueller theorem for symmetric bilinear torsions. Chin. Ann. Math. 29B (2008), 385-424.

A mod 2 index theorem for the twisted Signature operator. Science in China (Series A) 42 (1999), 1279-1285.

Sub-signature operator and its local index theorem. Chinese Sci. Bull. 41 (1996), 294-295. (in Chinese)

(with X. Ma) Eta-invariants, torsion forms and flat vector bundles. Math. Ann. 340 (2008), 569-624.

(with J. D. Lafferty and Y. Yu) Clifford asymptotics and the local Lefshetz index. Lect. Notes in Math. vol. 1411, pp. 137-142. Springer-Verlag, 1990.

(with H. Feng and W. Hu) A family quantization formula for symplectic manifolds with boundary. Science in China (Series A), 44 (2001), 599-609.

A remark on the regularity of the eta function of Dirac operators. Acta Math. Sinica (N. S.) 9 (1993), 240-245.

Local index theorem of Atiyah-Singer for families of Dirac operators. Lect. Notes in Math. vol. 1369, pp. 351-366. Springer-Verlag, 1989.

On the mod $k$ index theorem of Freed and Melrose. J. Diff. Geom. 43 (1996), 198-206.

A remark on a residue formula of Bott. Acta Math. Sinica (N.S.) 6 (1990), 306-314.

(with X. Dai) Real embeddings and the Atiyah-Patodi-Singer index theorem for Dirac operators. Asian J. Math. 4 (2000), 775-794.

The existence of Riemannian metrics with positive scalar curvature over complex hypersurface. Acta Math. Sinica (N. S.) 39 (1996), 460-462. (in Chinese)

(with X. Ma) Superconnection and family Bergman kernels. C. R. Acad. Sci. Paris, Serie I, 344 (2007), 41-44.

(with X. Ma) An anomaly formula for L^2-analytic torsions on manifolds with boundary. in Analysis, Geometry and Topology of Elliptic Operators. Eds. B. Booss-Bavnbek, S. Klimek, M. Lesch and W. Zhang, World Scientific, 2006, pp. 247-274.

(With X. Ma) Toeplitz quantization and symplectic reduction. in Differential Geometry and Physics. Eds. M.-L. Ge and Weiping Zhang, Nankai Tracts in Mathematics Vol. 10, World Scientific, 2006, pp. 343-349.

(With W. Li) An L^2 Alexander-Conway invariant for knots and the volume conjecture. in Differential Geometry and Physics. Eds. M.-L. Ge and Weiping Zhang, Nankai Tracts in Mathematics Vol. 10, World Scientific, 2006, pp. 303-312.

(with X. Dai) An index theorem for Toeplitz operators on odd dimensional manifolds with boundary. J. Funct. Anal. 238 (2006), 1-26.

(with W. Li) An L^2-Alexander invariant for knots. Commun. Contemp. Math. 8 (2006), 167-187.

(with X. Ma) Eta-invariant and flat vector bundles. Chin. Ann. Math. 27B (2006), 67-72.

(with X. Ma) Bergman kernels and symplectic reduction. C. R. Acad. Sci. Paris, Serie I, 341 (2005), 297-302.

An extended Cheeger-Mueller theorem for covering spaces. Topology 44 (2005), 1093-1131.

Eta-invariant and Chern-Simons current. Chin. Ann. Math. 26B (2005), 45-56.

(with F. Han) Modular invariance, characteristic numbers and $\eta$ invariants. J. Diff. Geom. 67 (2004), 257-288.

Sub-signature operators, eta-invariants and a Riemann-Roch theorem for flat vector bundles. Chin. Ann. Math. 25B (2004), 7-36.

Circle actions and Z/k-manifolds. C. R. Acad. Sci. Paris, Ser. I, 337 (2003), 57-60.

(with F. Han) Spin^c-manifolds and elliptic genera. C. R. Acad. Sci. Paris, Ser. I, 336 (2003), 1011-1014.

(with K. Liu and X. Ma) Rigidity and vanishing theorems in K-theory. Commun. Anal. Geom. 11 (2003), 121-180.

(with Z. Tang) A generalization of the Atiyah-Dupont vector fields theory. Commun. Contemp. Math. 4 (2002), 777-796.

Heat kernels and the index theorems on even and odd dimensional manifolds. Proc. ICM2002, Vol. 2, pp.361-369.

(With K. Liu and X. Ma) On elliptic genera and foliations. Math. Res. Lett. 8 (2001), 361-376.

(with K. Liu and X. Ma) Spin^c manifolds and rigidity theorems in K-theory. Asian J. Math. 4 (2000), 933-960.

(with K. Liu and X. Ma) Rigidity and vanishing theorems in K-theory. C. R. Acad. Sci. Paris, Serie I, 330 (2000), 301--306.

A counting formula for the Kervaire semi-characteristic. Topology 39 (2000), 643-655.

Symplectic reduction and family quantization. Inter. Math. Res. Notices (1999), No. 19, 1043-1056.

(with Y. Tian) Quantization formula for symplectic manifolds with boundary. Geom. Funct. Anal. 9 (1999), 596-640.

Analytic and topological invariants associated to nowhere zero vector fields. Pacific J. Math. 187 (1999), 379-398.

(with Y. Tian) Symplectic reduction and a weighted multiplicity formula for twisted Spin^c-Dirac operators. Asian J. Math. 2 (1998), 591-608.

(with Y. Tian) Holomorphic Morse inequalities in singular reduction. Math. Res. Lett. 5 (1998), 345-352.

(with X. Dai) Higher spectral flow. J. Funct. Anal. 157 (1998), 432-469.

(with Y. Tian) An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg. Invent. Math. 132 (1998), 229-259.

(with S. Wu) Equivariant holomorphic Morse inequalities III: non-isolated fixed points. Geom. Funct. Anal. 8 (1998), 149-178.

(with Y. Tian) Symplectic reduction and quantization. C. R. Acad. Sci. Paris, Serie I, 324 (1997), 433-438.

(with X. Dai) Splitting of the family index. Commun. Math. Phys. 182 (1996), 303-318.

(with X. Dai) Higher spectral flow. Math. Res. Lett. 3 (1996), 93-102.

(with X. Dai) Circle bundles and the Kreck-Stolz invariant. Trans. Amer. Math. Soc. 347 (1995), 3587-3593.

(with K. Liu) Elliptic genera and eta-invariant. Inter. Math. Res. Notices No. 8 (1994), 319-327.

(with J.-M. Bismut) Milnor and Ray-Singer metrics on the equivariant determinant of a flat vector bundle. Geom. Funct. Anal. 4 (1994), 136-212.

Circle bundles, adiabatic limits of eta invariants and Rokhlin congruences. Ann. Inst. Fourier 44 (1994), 249-270.

(with J.-M. Bismut) Real embeddings and eta invariant. Math. Ann. 295 (1993), 661-684.

(with J. D. Lafferty and Y. Yu) A direct geometric proof of the Lefschetz fixed point formula. Trans. Amer. Math. Soc. 329 (1992), 571-583.

A note on equivariant eta invariant. Proc. Amer. Math. Soc. 108 (1990), 1121-1129.