Research

Research Interest: Differential Geometry, Topology and Mathematical Physics

Publications and preprints:

Loop spaces, Field Theories and T-duality:

● (with Varghese Mathai) T-duality with H-flux for 2d sigma models, arXiv preprint.
● (with Varghese Mathai) T-duality, Jacobi forms and Witten Gerbe Modules, Advances in Theoretical and Mathematical Physics, 25 no. 5 (2021) 1235-1266.
● (with Varghese Mathai) Exotic Twisted Equivariant K-theory, J. Geom. Phys., 158 (2020), 103930.
● (with Varghese Mathai) T-duality, Vertical Holonomy Line Bundles and Loop Hori Formulae, Reviews in Mathematical Physics, Vol 33 (2022) 2250019, 25pp
● (with Varghese Mathai) T-duality in an H-flux: Exchange of Momentum and Winding, Comm. Math. Phys, Volume 363, no. 1 (2018) pp 333-350.
● (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 preprint.
● Supersymmetric Field Theories, Super Loop Spaces and Bismut-Chern Charater, arXiv preprint.

Some Mathematical Aspects of Anomaly Cancellations:
● (with Ruizhi Huang, Kefeng Liu and Weiping Zhang) Cubic Forms, Anomaly Cancellation and Modularity, Advances in Mathematics, 394 (2022), 108023.
● (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.
● (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) Modular Forms and Generalized Anomaly Cancellation Formulas, J. Geom. Phys., 62 (2012), pp. 1038-1053.
● (with Kefeng Liu) Gravitational Anomaly Cancellation and Modular Invariance, Alg. Geom. Top. 14 (2014) 91-113.

String, String^c Manifolds and Various Modular Invariants:
● (with Ruizhi Huang) Elliptic Genus and String Cobordism at Dimension 24, Pacific J. of Math, to appear.
● (with Ruizhi Huang) On Characteristic Numbers of 24 Dimensional String Manifolds, Math. Z, 300 (2022), no.3, 2309–2331.
● (with Ruizhi Huang and Varghese Mathai) Fractional Structures on Bundle Gerbe Modules and Fractional Classifying Spaces, arXiv preperint.
● (with Varghese Mathai) Projective Elliptic Genera and Elliptic Pseudodifferential Genera, Advances in Mathematics, 358 (2019), 1-25.
● (with Haibao Duan and Ruizhi Huang) String^c Structures and Modular Invariants, Trans. A.M.S, Volume 374, Number 5, May 2021, 3491-3533.
● (with Weiping Zhang) eta Invariant and Modular Forms, Quarterly Journal of Mathematics, 66 (2015), 133–142.
● (with Qingtao Chen and Weiping Zhang) Generalized Witten Genus and Vanishing Theorems, J. Diff. Geom. 88 (2011), 1-39.
● (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) Elliptic Genera, Transgression and Loop Space Chern-Simons Forms, Comm. Anal. Geom., Vol 17, No.1, Jan 2009, 73-106.

Rokhlin Type Divisibilities and Congruences:
● (with Qingtao Chen) Mod 3 Congruence and Twisted Signature of 24 Dimensional String Manifolds, Trans. A.M.S, 367 (2015), 2959-2977.
● (with Qingtao Chen) Modular Invariance and Twisted Cancellation of Characteristic Numbers, Trans. A. M. S. 361 (2009), no. 3, 1463-1493.
● (with Xiaoling Huang) Even Dimensional Manifolds and Generalized Anomaly Cancellation Formulas, Trans. A. M. S., 359 (2007), no. 11, 5365-5381.
● (with Weiping Zhang) Modular Invariance, Characteristic Numbers and eta Invariants, J. Diff. Geom. 67 (2004), 257-288.
● (with Weiping Zhang) Spin^c-manifold and Elliptic Genera. C. R. Acad. Sci. Paris, Serie I. 336 (2003), 1011-1014.

Group Actions and Rigidity:
● (with Varghese Mathai) Witten Genus and Elliptic Genera for Proper Actions, Comm. Math. Phys, Volume 389, (2022) 1215-1239.
● (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 Jianqing Yu) On the Witten Rigidity Theorem for Odd Dimensional Manifolds, arXiv preprint.
● (with Kefeng Liu and Weiping Zhang) E8 Bundles and Rigidity, arXiv preprint.

Curvature Conditions and Topological Obstructions:
● (with Xiaoyang Chen and Jian Ge) Almost Nonnegative Ricci Curvature and New Vanishing Theorems for Genera, Math. Z. 306 (2024), no. 3, Paper No. 44, 11 pp. https://link.springer.com/article/10.1007/s00209-024-03448-1
● (with Xiaoyang Chen) New Bochner Type Theorems, Math. Ann. 388, 3757–3783 (2024). https://link.springer.com/article/10.1007/s00208-023-02612-y

Miscellaneous:
● (with Hao Li and Zhi Lv) Iterated Residue, Toric Forms and Witten Genus, arXiv preprint.
● (with Jingfang Lian, Hao Li and Zhi Lv) Twisted Milnor Hypersurfaces, Pure and Applied Mathematics Quarterly, Volume 18, Number 3, 923–970, 2022.
● (with Qingtao Chen) Witten Genus and String Complete Intersections, Pacific J. of Math, Vol 234, No.2, Feb 2008, 249-260.

In preparation:

● (with Christopher Schommer-Pries, Stephan Stolz and Peter Teichner) Equivariant Cohomology via Gauged Field Theories, in preparation.
● (with Stephan Stolz and Peter Teichner) The Bismut-Chern Character Form as Dimension Reduction, in preparation.

Volumes Edit:

● (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.
● (jointly edit with Varghese Mathai, Guoliang Yu and Weiping Zhang), Index Theory, Duality and Related Fields, Special Issue of Journal of Geometry and Physics.