Long Qian

Mathematical logic · Carnegie Mellon University

Long Qian

Hi! I’m Long, a PhD student in mathematical logic at Carnegie Mellon University, advised by André Platzer. I study the logical foundations of differential equations through differential dynamic logic.

I am also interested in computer-assisted mathematics, particularly the application of automated reasoning tools to combinatorial problems. I have previously worked on classifying the complexity of geometric properties of Banach spaces.

Feel free to get in touch!

Publications Email Google Scholar CV
Portrait of Long Qian
PhD student in Pure and Applied Logic
Carnegie Mellon University · Since Fall 2021

Research

Logical foundations of continuous systems.

Computability & analysis

The algorithmic content of analysis, including the geometry and structure of computable Banach spaces.

Selected publications

All publications

Authors listed in alphabetical order.

  1. Accepted CSL · 2027

    Linear Axiomatization of Linear Differential Equations

    Long Qian and André Platzer

    A complete axiomatization for open properties of linear differential equations on compact initial sets and time horizons, reducing proofs to linear real arithmetic.

    BibTeX 
    @inproceedings{qian2027linear,
  title = {Linear Axiomatization of Linear Differential Equations},
  author = {Long Qian and André Platzer},
  year = {2027},
  booktitle = {EACSL Annual Conference on Computer Science Logic (CSL)},
  note = {Accepted, to appear}
}
    Logic & dynamics
  2. JACM · 2025

    Axiomatization of Compact Initial Value Problems: Open Properties

    André Platzer and Long Qianα

    A complete axiomatization of open safety, open liveness, and existence properties for compact initial value problems, connecting symbolic proofs with rigorous numerical error bounds.

    PDF arXiv DOI
    BibTeX 
    @article{platzer2025compact,
  title = {Axiomatization of Compact Initial Value Problems: Open Properties},
  author = {André Platzer and Long Qian},
  year = {2025},
  journal = {Journal of the ACM},
  volume = {72},
  number = {6},
  pages = {41:1--41:51},
  doi = {10.1145/3763228},
  eprint = {2410.13836},
  archivePrefix = {arXiv}
}
    Logic & dynamics
  3. CICM · 2025 Best Paper Award

    Automated Symmetric Constructions in Discrete Geometry

    Bernardo Subercaseaux, Ethan Mackey, Long Qian and Marijn Heule

    Embedding rotational symmetry into SAT encodings to discover new point configurations satisfying constraints in discrete geometry.

    PDF arXiv DOI
    BibTeX 
    @inproceedings{subercaseaux2025symmetric,
  title = {Automated Symmetric Constructions in Discrete Geometry},
  author = {Bernardo Subercaseaux and Ethan Mackey and Long Qian and Marijn Heule},
  year = {2025},
  booktitle = {International Conference on Intelligent Computer Mathematics (CICM)},
  pages = {29--47},
  doi = {10.1007/978-3-032-07021-0_3},
  eprint = {2506.00224},
  archivePrefix = {arXiv}
}
    Automated reasoning