Topologize  Life      -hold the Euler characteristic of soul

Biography:

I am a tenured associate professor from Apr. 2022 at Academy of Mathematics and Systems Science, Chinese Academy of Sciences. 

In the same institute, I was an assistant professor from 2020-2022 working on Homotopy of manifolds and Topological aspects of index theory, and was a postdoc from 2018-2020 mainly on manifold topology and index theorem mentored by Prof. Haibao Duan, Prof. Fei Han (NUS), and Prof. Jianzhong Pan.

I got my PhD degree at Department of Mathematics of National University of Singapore at Nov. 2017, under the supervision of Prof. Jie Wu on unstable homotopy theory.

From 2011 to 2014, I was working with Prof. Xiugui Liu in Nankai University as a master student on rational homotopy theory. 

I got the diploma of material physics at Dalian University of Technology in 2007, and thereafter worked in two electric companies in Shenyang as technologist and designer from 2008-2010.

Research Interests:

Algebraic topology and applications in manifold topology, differential geometry and mathematical physics, etc.

My collaborators:

Guy Boyde, Frederick R. Cohen, Haibao Duan, Fei Han, Pengcheng Li, Kefeng Liu, Xiugui Liu, Zhi Lu, Varghese Mathai, Jianzhong Pan, Yang Su, Stephen Theriault, Jie Wu, Weiping Zhang

Books:

• (with Stephen Theriault), Loop spaces decompositions, >300pages, in preparation, to appear in World Scientific Publishing Co. Pte. Ltd.

Papers:

Loop Homotopy of Manifolds:    

[Ω1] (with Stephen Theriault) homotopy of blow ups after looping, 41 pages, arXiv:2308.14531. 

[Ω2] Sphere bundles over 4-manifolds are trivial after looping, 10 pages, arXiv:2210.17352. 

[Ω3] (with Stephen Theriault) Homotopy of manifolds stabilized by projective spaces, Journal of  Topology, vol 16 issue 3 (2023), 1237-1257.  arXiv:2204.04368 

[Ω4] (with Stephen Theriault), An extended rational dichotomy for certain open books, 14 pages, submitted, arXiv:2111.07063

[Ω5] Loop homotopy of 6-manifolds over 4-manifolds, Algebraic and Geometric Topology 23 (5) (2023), 2369-2388. arXiv:2105.03881

[Ω6] (with Stephen Theriault), Loop space decompositions of (2n-2)-connected (4n-1)-dimensional Poincare Duality complexes, Research in the Mathematical Sciences volume 9, Article number: 53 (2022).  arXiv:2106.08055

Unstable homotopy theory:

[P1] (with Guy Boyde) Some asymptotic formulae for torsion in homotopy groups, 19 pages, to appear in Canadian Journal of Mathematics. arXiv:2301.02497

[P2] (with Stephen Theriault), Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups, 16 pages, to appear in Annales de l'Institut Fourier. arXiv:2105.04426  

[P3] (with Fred Cohen), Orders of the canonical vector bundles over configuration spaces of finite graphs, Pacific Journal of Mathematics, Vol. 316 No. 1 (2022), 53-64. arXiv: 2110.12688

[P4] (with Jie Wu), Exponential growth of homotopy groups of suspended finite complexes, Mathematische Zeitschrift 295, (2020), 1301-1321. arXiv:1706.02918 

[P5] (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

[P6] (with Jie Wu), Cancellation and homotopy rigidity of classic functors, Journal of the London Mathematical Society 99 (1) (2019), 225-248. arXiv:1706.02917

[P7] (with Jie Wu), On mod $p$ $A_p$-spaces, Algebraic and Geometric Topology 17 (2017), 2125-2144. arXiv:1701.05803, PDF

Manifold topology, index theory and mathematical physics:    

[AS1] (with Fei Han and Varghese Mathai), Fractional structures on bundle gerbe modules and fractional classifying spaces, 54 pages, preprint, 2022, arXiv:2203.14439

[AS2] (with Fei Han), Elliptic genus and string cobordism at dimension 24, 10 pages, preprint, 2012, arXiv:2110.11022

[AS3] (with Fei Han), On characteristic numbers of 24 dimensional string manifolds, Mathematische Zeitschrift 300 (2022), 2309-2331. arXiv:2103.11413

[AS4] (with Fei Han, Kefeng Liu and Weiping Zhang), Cubic forms, anomaly cancellation and modularity, Advances in Mathematics, 394 (2022) 108023. arXiv:2005.02344

[AS5] (with Haibao Duan and Fei Han), String^c structures and modular invariants, Transactions of the American Mathematical Society, Volume 374, Number 5, May 2021, 3491-3533.  arXiv:1905.02093

Suspension Homotopy of Manifolds and Gauge Groups:    

[Σ1] (with Pengcheng Li) Suspension homotopy of simply connected 7-manifolds, 27 pages, arXiv:2208.13145 

[Σ2] Suspension homotopy of 6-manifolds, Algebraic and Geometric Topology  23 (1) (2023), 439-460. arXiv:2104.04994

[Σ3] Homotopy types of gauge groups over high dimensional manifolds, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 152, 182-208 (2022). arXiv:1805.04879

[Σ4] Homotopy of gauge groups over non-simply-connected five dimensional manifolds, Science China Mathematics, Vol. 64 No. 5, 1061-1092, (2021). arXiv:1805.04878

Rational homotopy theory:             

[Q1=Ω4] (with Stephen Theriault), An extended rational dichotomy for certain open books, 14 pages, submitted, arXiv:2111.07063

[Q2=P2] (with Stephen Theriault), Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups, 16 pages, to appear in Annales de l'Institut Fourier. arXiv:2105.04426    

[Q3] Coformality around fibrations and cofibrations, 13 pages, Homology, Homotogy and Applications 25 (1) (2023), 235-248. arXiv:2108.08446

[Q4] (with Xiugui Liu), Some notes on the sectional fibrations, Topology and its Applications 207 (2016), 123-135. PDF

[Q5] (with Xiugui Liu), The rational homotopical nilpotency of principal $U_n(\mathbb{C})$-bundles, Topology and its Applications 160 (2013), 1466-1475. PDF

Some computations during master study:             

[S1] (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. PDF 

[S2] (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. PDF

[S3] (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.

In preparation:

• (with Stephen Theriault) "Homotopy of certain manifolds'', in preparation.

• (with Fei Han) "Index theoretical aspects of some topological numeric invariants", in preparation.

• (with Haibao Duan) Equivariant degrees of maps from spheres to complex Stiefel manifolds, 14 pages.