Lipcaty

About me

My name is Pengcheng Li (李鹏程). I am a young algebraic topologist in Department of Mathematics, School of Sciences of Great Bay University, as an assistant professor. In June 2020, I received my Ph.D. from the Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences (AMSS, CAS) under the supervision of Jianzhong PAN.

My main research interests lie in classical homotopy theory; I am particularly interested in the homotopy theory of $(n-1)$-connected $(n+2)$-dimensional finite CW-complexes (called $\mathbf{A}_n^2$-complexes) and its applications, such as modular cohomotopy groups, homotopy types of suspended or looped manifolds.

E-mail: lipcaty@outlook.com
CV
GBU Topology
GBU webpage

Education and Employments

  • 03/2023~present: Assistant professor, Department of Mathematics, School of Sciences, Great Bay University.
  • 03/2021~ 02/2023: Postdoc in Department of Mathematics, Southern University of Science and Technology; mentor: Yifei Zhu
  • 09/2020~01/2021: Visiting scholar in Hebei Normal University; mentor: Jie Wu (now in BIMSA)
  • 09/2015~06/2020: Ph.D. in Pure Mathematics, AMSS, CAS; advisor: Jianzhong Pan.
  • 09/2011~07/2015: B.S. in Mathematics and Applied Mathematics, School of Mathematics, Dalian University of Technology.

Collaborators

Zhongjian Zhu, Ruizhi Huang, Jianzhong Pan, Jie Wu

Publications

  1. Periodic problem on homotopy groups of Chang complexes $C^{n+2,r}_r$, Homology, Homotopy and Applications, vol. 21(2), 2019: 363-375. (with Zhongjian Zhu and Jianzhong Pan).

  2. (Co)Homology self-closeness numbers of simply-connected spaces, Homology, Homotopy and Applications, vol. 23(1), 2020: 1-16.

  3. On Modular Cohomotopy Groups, Israel Journal of Mathematics, vol. 253, 2023: 887–915. (with Jianzhong Pan and Jie Wu).

  4. Self-closeness numbers of product spaces, Homology, Homotopy and Applications, vol. 25 (1), 2023: 249-264.

  5. Homotopy Types of Suspended 4-manifolds, Algebraic and Geometric Topology, vol. 24 (2024), Issue 5: 2933-2956.

  6. The Homotopy Decomposition of the Suspension of a non-simply-connected 5-manifold, to appear in Proceedings of the Royal Society of Edinburgh Section A: Mathematics. (with Zhongjian Zhu).

  7. Cohomotopy Sets of $(n-1)$-connected $(2n+2)$-manifolds for small $n$, to appear in Transactions of London Mathematical Society, vol. 253, 2023: 887-915. (with Jianzhong Pan and Jie Wu).

  8. Suspension splitting and cohomotopy sets of simply connected $7$-manifolds, to appear in Canadian Journal of Mathematics. (with Ruizhi Huang).

  9. The Homotopy Types of Suspended Simply-connected 6-manifolds, to appear in Homology, Homotopy and Applications. (with Zhongjian Zhu).

Teaching

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