Publications

  1. Preprint
    Positive Sectional Curvature on All Smooth 7-Spheres
    Yang-Hui He, Ziran Liu, and Shing-Tung Yau
    Preprint, 2026
    arXiv PDF
  2. NeurIPS
    CORA: Per-Slice Coherent Orthogonal Rotation for SVD-based Low-Rank Adaptation
    Pengcheng Wang, Ziran Liu, Wei Wang, and Wei Jiang
    Accepted at the 40th Annual Conference on Neural Information Processing Systems (NeurIPS 2026), 2026
    arXiv PDF
  3. Preprint
    Persistent Mixed Worldviews in the Theory of Chosen Preferences
    Ziran Liu
    Preprint, 2026
    arXiv PDF
  4. Preprint
    Shannon’s Problem on the Monotonicity of Entropy and a Conjecture of Tao
    Ziran Liu
    Preprint, 2026
    arXiv PDF
  5. Preprint
    Atiyah’s Minkowski Space Conjecture Fails for Every n\ge3
    Ziran Liu
    Preprint, 2026
    arXiv PDF
  6. Submitted
    Nonexistence of vanishing-viscosity limits for mechanical Hamiltonian ergodic problems
    Ziran Liu, Hung V. Tran, and Yifeng Yu
    Submitted for Publication, 2026
    arXiv PDF
  7. Preprint
    Stationary Distributions for the Nonsemimartingale Reflected Brownian Motion with Drift in a Wedge: Exact Logarithmic Tails
    Ziran Liu
    Preprint, 2026
    arXiv PDF
  8. Preprint
    Stationary Distributions for the Nonsemimartingale Reflected Brownian Motion with Drift in a Wedge: Existence, Classification and Elliptic PDE Obstructions
    Ziran Liu
    Preprint, 2026
    arXiv PDF
  9. Preprint
    Arithmetic Concentration and Gaussian Fluctuations for Random Windows of Elliptic-Curve Congruential Generators
    Ziran Liu and Chung Pang Mok
    Preprint, 2026
    arXiv PDF
  10. Submitted
    On discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator
    Ziran Liu and Chung Pang Mok
    Submitted for Publication, 2026
    arXiv PDF
  11. Submitted
    Sharp global and almost everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations
    Ziran Liu, Hung V. Tran, and Yifeng Yu
    Submitted for Publication, 2026
    arXiv PDF
  12. Submitted
    Geometric and Spectral Alignment for Deep Neural Network II
    Ziran Liu, Wei Wang, Jinhao Wang, Pengcheng Wang, Xinyi Sui, Cihan Ruan, Nam Ling, and Wei Jiang
    Submitted for Publication, 2026
    arXiv PDF
  13. Submitted
    Geometric and Spectral Alignment for Deep Neural Network I
    Ziran Liu, Wei Wang, Jinhao Wang, Pengcheng Wang, Xinyi Sui, Cihan Ruan, Nam Ling, and Wei Jiang
    Submitted for Publication, 2026
    arXiv PDF
  14. Preprint
    Joint thick-point content for log-correlated fields
    Ziran Liu
    Preprint, 2026
    PDF
  15. Submitted
    Joint Multifractal Spectra for Correlated Gaussian Multiplicative Chaos and an Application to Circular β-Ensembles
    Ziran Liu
    Submitted for Publication, 2026
    PDF
  16. Submitted
    Gaussian Chaos Noise: Variational Design of Noise Regularizers for Reliable Deep Learning
    Ziran Liu, Jinhao Wang, Wei Wang, and Wei Jiang
    Submitted for Publication, 2026
    PDF
  17. Submitted
    Approaching the Prescribed Gaussian Curvature by Discrete Conformality
    Ziran Liu and Tianqi Wu
    Submitted for Publication, 2024
    arXiv PDF
  18. Article
    Reflected Brownian Motion with Drift in a Wedge
    Peter Lakner, Ziran Liu, and Josh Reed
    Queueing Systems, 2023
    Bib PDF
  19. Thesis
    Reflected Brownian Motion and its Applications to Differential Geometry and Index Theory
    Ziran Liu
    May 2023
    PDF
  20. Thesis
    Stationary Gaussian Processes and the Kolmogorov-Wiener Prediction Problem
    Ziran Liu
    May 2016
    PDF
  21. Thesis
    Lichnerowicz Type Vanishing Theorem for Mathai-Zhang Index
    Ziran Liu
    Jun 2014
    PDF