Rui Chen

PhD Student in Mathematics

Analysis & Geometry

Nonlocal operators,
spectral theory &
geometric analysis.

I am a PhD student in mathematics, currently working on nonlocal operators, functional inequalities, spectral theory, and partial differential equations, with a particular interest in fractional and logarithmic operators on Euclidean spaces, manifolds, and graphs.

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About my research

About

Welcome to my personal webpage. My research lies in analysis and geometry, with a focus on nonlocal operators such as the fractional Laplacian, the logarithmic Laplacian, and the fractional-logarithmic Laplacian. I am particularly interested in the partial differential equations, functional inequalities, and spectral theory associated with these operators, especially in the settings of manifolds and discrete graphs.

I’m always happy to chat about mathematics, exchange ideas, and explore possible collaborations.

Research & Publications

Four Research Directions

Explore the questions and papers behind each research direction.

Nonlocal Operators and Their Applications

Fractional, logarithmic and fractional-logarithmic operators: their fundamental properties, potential theory, and applications on spaces, manifolds and graphs.

5 publications
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Showing 2 of 5 publications

Spectral Theory and Functional Inequalities

Eigenvalues, fundamental gaps, eigenfunction estimates, and functional inequalities for local and nonlocal operators.

4 publications
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Showing 2 of 4 publications

Elliptic and Parabolic Equations

Least-energy solutions, lifespan and threshold phenomena, and long-time asymptotics for heat and fractional heat equations.

3 publications
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Showing 2 of 3 publications

Geometric and Harmonic Analysis

Riesz transforms, heat semigroups, and stochastic completeness on complete Riemannian manifolds.

2 publications

Showing 2 of 2 publications

Education

  • Oct 2025 – Present
    Visiting Ph.D. Student, Brandenburg University of Technology Cottbus-Senftenberg, Germany
    Advisor: Daniel Hauer
  • Aug 2023 – Present
    Ph.D. in Mathematics, Fudan University, China
    Advisor: Bobo Hua
  • Sep 2019 – Jun 2023
    B.Sc. in Mathematics and Applied Mathematics, Central South University, China

Talks & Visits

Invited Talks

  • Shanghai Institute for Mathematics and Interdisciplinary Sciences; one-hour invited talk
    Shanghai, China
    22.06.2026
  • School of Mathematics and Statistics, Central South University; one-hour invited talk
    Changsha, China
    15.06.2026
More invited talks (3)
  • 13th International Conference on Nonlinear Analysis, Function Spaces and Applications
    Prague, Czech Republic
    01.06.2026–05.06.2026
  • Chinese–German Analysis and PDE Online Seminar
    Online Seminar
    Organizers: Huyuan Chen, Daniel Hauer, Jun Wang
    21.05.2026
  • 2024 Fudan-USTC Spectral Geometry Conference
    University of Science and Technology of China, China
    29.11.2024–01.12.2024

Research Visits

  • Brandenburg University of Technology Cottbus-Senftenberg
    Germany
    Oct 2025 – Present

Selected Workshops and Conferences

7 events

Selected Workshops and Conferences

  • Young Researchers in Ferrara: Between Analysis and Geometry
    Ferrara, Italy
    12.10.2026 – 14.10.2026
  • Second Research Meeting of Analysis
    Brandenburg University of Technology Cottbus-Senftenberg, Germany
    07.04.2026 – 09.04.2026
  • Horizons in Nonlinear PDEs Spring School
    Ulm University, Germany
    09.03.2026 – 13.03.2026
  • Annual Meeting of Analysis
    Brandenburg University of Technology Cottbus-Senftenberg, Germany
    23.01.2026 – 25.01.2026
  • 2025 International Workshop on Fully Nonlinear Partial Differential Equations
    Shanghai Institute of Mathematics and Interdisciplinary Studies, China
    16.06.2025 – 20.06.2025
  • The 32nd Yangtse River Conference on PDEs
    Anhui Normal University, China
    30.05.2025 – 01.06.2025
  • 2023 Fudan-USTC Spectral Geometry Conference
    Fudan University, China
    November 2023

Research Keywords

Research Keywords

Fractional Laplacian Logarithmic Laplacian Spectral Theory Geometric Analysis PDE Manifolds Graphs Variational Methods Inequality

Contact

I’m always happy to chat about mathematics, exchange ideas, and explore possible collaborations. Feel free to get in touch by email.

Location: Germany / China