Institute of Mathematics, AMSS, Chinese Academy of Sciences,
No.55 ZhongGuanCun East Road, Beijing 100190, P. R. China.

Officie : 1012 Siyuan building
E-mail: huangrz AT amss.ac.cn

Research Interests
Algebraic topology and applications related to manifold topology, differential geometry and mathematical physics, etc.

Employment
2020--      Institute of Mathematics, AMSS, CAS, assistant professor.
2018--2020  Institute of Mathematics, AMSS, CAS, post-doc. Mentors : Haibao Duan, Fei Han (NUS), and Jian Zhong Pan.

2009--2010  Shenyang Huali Electric Group, Shenyang, designer.

2008--2009  New Northeast Electric Group CO.LTD, Shenyang, technologist

Education
2014- 2017  PhD. in Mathematics, National University of Singapore, Advisor: Jie Wu.
2011--2014  Master's degree in Mathematics, Nankai University, Advisor: Xiugui Liu
2003--2007  Bachelor's degree in Material Physics, Dalian University of Technology

Teaching

Algebraic Topology I, II, AMSS, Spring 2022, instructor

Basic Topology, UCAS, 2018-2021, tutor

Seminar Course on Geometry and Topology, UCAS, 2019-2021, TA

Calculus (2015), Introductory Mathematics (2016), Mathematics II (2017), NUS, tutor

Publications:

I) Manifold topology, index theory and mathematical physics:

[1] (with Fei Han, Varghese Mathai), Fractional structures on bundle gerbe modules, 40+ pages, arXiv: to appear.

[2] (with Fei Han), On characteristic numbers of 24 dimensional String manifolds, 23 pages, to appear in Mathematische Zeitschrift (2021), https://doi.org/10.1007/s00209-021-02877-6, arXiv:2103.11413

[3] (with Fei Han, Kefeng Liu and Weiping Zhang), cubic forms, anomaly cancellation and modularity, 46 pages, to appear in Advances in Mathematics (2021), https://doi.org/10.1016/j.aim.2021.108023 ,arXiv:2005.02344

[4] (with Haibao Duan and Fei Han), String^c structures and modular invariants, 43 pages, Transactions of the American Mathematical Society, Volume 374, Number 5, May 2021, 3491-3533. arXiv:1905.02093

[5] (with Fei Han), Elliptic genus and string cobordism at dimension $24$, 10 pages, arXiv: 2110.11022

II) Homotopy aspects of manifolds:

[6] (with Stephen Theriault), An extended rational dichotomy for certain open books, 14 pages, submitted, arXiv:2111.07063

[7] Loop homotopy of 6-manifolds over 4-manifolds, 20 pages, to appear in ​Algebraic and Geometric Topology. arXiv:2105.03881

[8] Suspension homotopy of 6-manifolds, 19 pages, to appear in Algebraic and Geometric Topology. arXiv:2104.04994

[9] (with Stephen Theriault), Loop space decompositions of (2n-2)-connected (4n-1)-dimensional Poincare Duality complexes, submitted, arXiv:2106.08055

[10] Homotopy types of gauge groups over high dimensional manifolds, 32 pages, to appear in Proceedings of the Royal Society of Edinburgh Section A: Mathematics. arXiv:1805.04879

[11] Homotopy of gauge groups over non-simply-connected five dimensional manifolds, 33 pages, to appear in Science China Mathematics. arXiv:1805.04878

III) Unstable homotopy theory:

[12] (with Stephen Theriault), Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups, 12 pages, submitted. arXiv:2105.04426

[13] (with Fred Cohen), Orders of the canonical vector bundles over configuration spaces of finite graphs, 12 pages, to appear in Pacific Journal of Mathematics (2021).

[14] (with Jie Wu), Exponential growth of homotopy groups of suspended finite complexes, Mathematische Zeitschrift 295 (2020), 1301-1321. arXiv:1706.02918

[15] (with Jie Wu), Combinatorics of double loop suspensions, evaluation maps and Cohen groups, Journal of the Mathematical Society of Japan Vol. 72, No. 3 (2020), pp. 847-889. arXiv:1706.02916

[16] (with Jie Wu), Cancellation and homotopy rigidity of classic functors, Journal of the London Mathematical Society 99 (1) (2019), 225-248. arXiv:1706.02917

[17] (with Jie Wu), On mod $p$ $A_p$-spaces, Algebraic and Geometric Topology 17 (2017), 2125-2144.arXiv:1701.05803

IV) Stable and Rational homotopy theory:

[18] Coformality around fibrations and cofibrations, 13 pages, preprint, 2021, arXiv:2108.08446.

[19] (with Xiugui Liu), Some notes on the sectional fibrations, Topology and its Applications 207 (2016), 123-135.

[20] (with Xiugui Liu), Non-triviality of a product in the Adams $E_2$-term, Indian Journal of Pure and Applied Mathematics, vol. 47 (1) (2016), 59-72.

[21] (with Xiugui Liu), A nontrivial product in the $E_2$-term of the Adams spectral sequence for the sphere spectrum, Journal of Homotopy and Related Structures, vol. 10 (4) (2015), 735-748.

[22] (with X. Liu and S. Liu), Existence of $b_0b_1g_0\gamma_s$-element in the stable homotopy of spheres, Journal of Homotopy and Related Structures, vol. 9 (2) (2014), 263-271.

[23] (with Xiugui Liu), The rational homotopical nilpotency of principal $U_n(\mathbb{C})$-bundles, Topology and its Applications 160 (2013), 1466-1475.