Research Interest: Differential Geometry, Topology and Mathematical Physics

 

Research Papers:

 

Equivariant Cohomologies and Gauged Field Theories:

[1] (with Christopher Schommer-Pries, Stephan Stolz and Peter Teichner) Equivariant Cohomology via Gauged Field Theories, in preparation. 

 

Bismut-Chern Character and Chern Character:

[2] (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.

[3] (with Daniel Berwick-Evans)  The Equivariant Chern Character as Super Holonomy on Loop Stacks, arXiv:1610.02362, submitted

[4] (with Stephan Stolz and Peter Teichner) The Bismut-Chern Character Form as Dimension Reduction, in preparation.

[5] 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:

[6] (with Qingtao Chen) Elliptic Genera, Transgression and Loop Space Chern-Simons Forms, Comm. Anal. Geom., Vol 17, No.1, Jan 2009, 73-106.

[7] (with Weiping Zhang) eta Invariant and Modular Forms, Quarterly Journal of Mathematics, 66 (2015), 133–142.

 

 

Rokhlin Type Divisibilities and Congruences:

[8] (with Weiping Zhang) Spin^c-manifold and Elliptic Genera. C. R. Acad. Sci. Paris, Serie I. 336 (2003), 1011-1014.

[9] (with Weiping Zhang) Modular Invariance, Characteristic Numbers and eta invariants, J. Diff. Geom. 67 (2004), 257-288.

[10] (with Xiaoling Huang) Even Dimensional Manifolds and Generalized Anomaly Cancellation Formulas, Trans. A. M. S., 359 (2007), no. 11, 5365-5381.

[11] (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:

[12] (with Kefeng Liu and Weiping Zhang) E8 Bundles and Rigidity, arXiv:1307.6137, submitted.

[13] (with Jianqing Yu) On the Witten Rigidity Theorem for Odd Dimensional Manifolds, arXiv:1504.03007, submitted.

[14] (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.

 

String Manifolds:

[15] (with Qingtao Chen) Witten Genus and String Complete Intersections, Pacific J. of Math, Vol 234, No.2, Feb 2008, 249-260.

[16] (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.

[17] (with Qingtao Chen and Weiping Zhang) Generalized Witten Genus and Vanishing Theorems,  J. Diff. Geom. 88 (2011), 1-39.

[18] (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:

[19] (with Kefeng Liu) Gravitational Anomaly Cancellation and Modular Invariance, Alg. Geom. Top. 14 (2014) 91-113.

[20] (with Kefeng Liu and Weiping Zhang) Modular Forms and Generalized Anomaly Cancellation Formulas, J. Geom. Phys., 62 (2012), pp. 1038-1053.

[21] (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.

[22] (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.

Books:

 

[1] (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.