Research Interest: Differential Geometry, Topology and Mathematical Physics
Equivariant Cohomologies and Gauged Field Theories:
 (with Christopher Schommer-Pries, Stephan Stolz and Peter Teichner) Equivariant Cohomology via Gauged Field Theories, in preparation.
Bismut-Chern Character and Chern Character:
 (with Varghese Mathai) Exotic Twisted Equivariant Cohomology of Loop Spaces, Twisted Bismut-Chern Character and T-duality, Comm. Math. Phys, Volume 337, Issue 1 (2015), pp 127-150.
 (with Daniel Berwick-Evans) The Equivariant Chern Character as Super Holonomy on Loop Stacks, arXiv:1610.02362, submitted
 (with Stephan Stolz and Peter Teichner) The Bismut-Chern Character Form as Dimension Reduction, in preparation.
 Supersymmetric Field Theories, Super Loop Spaces and Bismut-Chern Charater, arXiv: 0711.3862 (part of this paper will be incorporated into the above paper) .
Modular Transgression and Modular eta Invariant:
 (with Qingtao Chen) Elliptic Genera, Transgression and Loop Space Chern-Simons Forms, Comm. Anal. Geom., Vol 17, No.1, Jan 2009, 73-106.
 (with Weiping Zhang) eta Invariant and Modular Forms, Quarterly Journal of Mathematics, 66 (2015), 133–142.
Rokhlin Type Divisibilities and Congruences:
 (with Weiping Zhang) Spin^c-manifold and Elliptic Genera. C. R. Acad. Sci. Paris, Serie I. 336 (2003), 1011-1014.
 (with Weiping Zhang) Modular Invariance, Characteristic Numbers and eta invariants, J. Diff. Geom. 67 (2004), 257-288.
 (with Xiaoling Huang) Even Dimensional Manifolds and Generalized Anomaly Cancellation Formulas, Trans. A. M. S., 359 (2007), no. 11, 5365-5381.
 (with Qingtao Chen) Modular Invariance and Twisted Cancellation of Characteristic Numbers, Trans. A. M. S. 361 (2009), no. 3, 1463-1493.
Group Actions and Rigidity:
 (with Kefeng Liu and Weiping Zhang) E8 Bundles and Rigidity, arXiv:1307.6137, submitted.
 (with Jianqing Yu) On the Witten Rigidity Theorem for Odd Dimensional Manifolds, arXiv:1504.03007, submitted.
 (with Junwei Guo) On Certain Multi-variable Rational Identities Derived from the Rigidity of Signature of Manifolds , J. Math. Anal. Appl. 453 (2017) 360–365.
 (with Qingtao Chen) Witten Genus and String Complete Intersections, Pacific J. of Math, Vol 234, No.2, Feb 2008, 249-260.
 (with Qingtao Chen and Weiping Zhang) Witten Genus and Vanishing Results on Complete Intersections, C. R. Acad. Sci. Paris, Serie I. 348 (2010), 295-298.
 (with Qingtao Chen and Weiping Zhang) Generalized Witten Genus and Vanishing Theorems, J. Diff. Geom. 88 (2011), 1-39.
 (with Qingtao Chen) Mod 3 Congruence and Twisted Signature of 24 Dimensional String Manifolds, Trans. A.M.S, 367 (2015), 2959-2577.
Some Mathematical Aspects of Anomaly Cancellations:
 (with Kefeng Liu) Gravitational Anomaly Cancellation and Modular Invariance, Alg. Geom. Top. 14 (2014) 91-113.
 (with Kefeng Liu and Weiping Zhang) Modular Forms and Generalized Anomaly Cancellation Formulas, J. Geom. Phys., 62 (2012), pp. 1038-1053.
 (with Kefeng Liu and Weiping Zhang) Anomaly Cancellation and Modularity, Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics, In Memory of Gu Chaohao, World Scientific Publishing Co., Inc.
 (with Kefeng Liu and Weiping Zhang) Anomaly Cancellation and Modularity II. The E8 x E8 case, Sci. China Math. 60 (2017), no. 6, 985–994.
 (jointly edit with Xingwang Xu and Weiping Zhang) Geometric Analysis Around Scalar Curvatures, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore: Vol 31, World Scientific.