Liang Guo

Liang Guo

Liang Guo’s Homepage

Welcome to my homepage!

Address: Shanghai Institute for Mathematics and Interdisciplinary Science (SIMIS), Shanghai, 200433, China

E-mail: liangguo@simis.cn

Position: Postdoc

Research area

Higher index theory and Noncommutative geometry with the following topics:

  1. The equivariant coarse Baum-Connes conjecture for group actions;
  2. (Geometric) property (T) and applications;
  3. Ideal structure of Roe algebras;
  4. Nonstandard analysis and limit space theory;
  5. Coarse geometry of subspaces of $\ell^p$-spaces.

Education and Work experience

  • Ph.D in Mathematics, East China Normal University, 2018-2024
    • Advisor: Professor Qin Wang

  • B.S. in Mathematics, Jilin University, 2014-2018

  • 2024-now: Shanghai Institute for Mathematics and Interdisciplinary Sciences. (SIMIS), Postdoc

Mathscinet link: Guo, Liang3 - MathSciNet

Researchgate link: Liang Guo

Publications

  1. L. Guo, Q. Wang, and C. Zhang, The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure, to appear in J. Noncommut. Geom.. [2408.06660] The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure
  2. J. Deng, L. Guo, Q. Wang, and G. Yu, Higher index theory for spaces with an FCE-by-FCE structure. J. Funct. Anal., 288(1): Paper No. 110679, 2025. Link
  3. L. Guo, Z. Luo, Q. Wang, and Y. Zhang, A Bott periodicity theorem for $\ell^p$-spaces and the coarse Novikov conjecture at infinity. J. Funct. Anal., 286(2): Paper No. 110215, 2024. Link
  4. L. Guo, Z. Luo, Q. Wang, and Y. Zhang, $K$-theory of the maximal and reduced roe algebras of metric spaces with A-by-CE coarse fibrations. J. Topol. Anal., 16(6):989–1016, 2024. Link
  5. L. Guo, Z. Luo, Q. Wang, and Y. Zhang, The twisted coarse Baum-Connes conjecture with coefficients in coarsely proper algebras. J. Funct. Anal., 285(8): Paper No. 110067, 41, 2023. Link
  6. L. Guo, H. Wang, and Q. Wang, On the quotients of coarse structures and Roe algebras. Topology Appl., 319: Paper No. 108227, 18, 2022 Link

Preprint

  1. L. Guo, Q. Wang. Geometric Banach property (T) for metric spaces via Banach representations of Roe algebras, arxiv: 2505.02338 [2505.02338] Geometric Banach property (T) for metric spaces via Banach representations of Roe algebras
  2. L. Guo, J. Qian, Q. Wang, An ultraproduct approach to limit space theory, arXiv:2412.08130.[2412.08130] An ultraproduct approach to limit space theory
  3. L. Guo, Q. Wang, J. Wu and G. Yu, Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture. arXiv:2411.18538.[2411.18538] Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture
  4. J. Deng and L. Guo, Twisted Roe algebras and their K-theory. arXiv:2409.16556.[2409.16556] Twisted Roe algebras and $K$-theory

Conference and Seminar Talks

2024.

  • Noncommutative Geometry Seminar, Texas A&M University, TX, USA, 2024 03.28
    • Title: Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture.
  • Analysis Seminar, SUNY at Buffalo, NY, USA, 2024 04.03
    • Title: Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture.
  • The China-Japan-Korea Conference on Functional Analysis, Harbin Institute for Technology (HIT), Harbin, China, 2024 08.11-08.17.
    • Title: A Bott periodicity theorem for $\ell^p$-spaces and the coarse Novikov conjecture at infinity.
  • 第十三届全国算子理论与算子代数会议, 山西大学, 太原, 2024 08.19-08.23.
    • Title: Extensions of fibred coarsely embeddable spaces and higher index theory.
  • Operator algebras Seminar, Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS), Shanghai, China, 2024 09.26
    • Title: Twisted Roe algebras and their K-theory.
  • Analysis Seminar, Fudan University, Shanghai, China, 2024 10.31
    • Title: A Bott periodicity theorem for $\ell^p$-spaces and the coarse Novikov conjecture at infinity.

2025.

  • Workshop on Noncommutative Geometry and Operator Theory, Chengdu, China, 2025. 5.10
  • Title: Geometric Banach property (T) for metric spaces via Banach representations of Roe algebras

Teaching

Spring Semester 2025, Large Scale Geometry, SIMIS Room 1710, Every Monday 13:30-15:00