Zhe Su

Zhe Su's Picture

Department of Mathematics & Statistics, Auburn University
Office: 304 Parker Hall
E-mail: zhs0011@auburn.edu
URL : https://zhesu1.github.io/

About Me

I am an Assistant Professor at Auburn University. Previously, I was a research associate at Michigan State University working with Guowei Wei . Before that, I held a postdoc position at the University of California, Los Angeles, where I worked with Shantanu Joshi. I completed my PhD at Florida State University under the supervision of Eric Klassen and Martin Bauer. My research background lies in the application of differential geometry to topological data analysis and shape analysis. I am interested in developing geometric and topological methods and computational tools for data analysis and machine learning. In particular, I focus on topological data analysis on manifolds via de Rham–Hodge theory, and on geometric shape analysis of curves and surfaces with applications to statistics on manifolds.

Research Interests

Mathematical AI, Topological Data Analysis, Computational Topology, Shape Analysis, Statistics on Manifolds, Machine Learning, Differential Geometry

Preprints

  1. Z. Su, X. Liu, L. Bou Hamdan, V. Maroulas, J. Wu, G. Carlsson, G.-W. Wei. Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology - A Review. arXiv:2507.19504, submitted.
  2. X. Liu, Z. Su, Y. Shi, Y. Tong, G. Wang, G.-W. Wei. Manifold Topological Deep Learning for Biomedical Data. arXiv:2503.00175, submitted.

Published Articles

  1. D. Chen, J. Jiang, N. Hayes, Z. Su, G.-W. Wei. Artificial intelligence approaches for anti-addiction drug discovery. Digital Discovery , 4, (2025)
    doi:10.1039/D5DD00032G, arXiv:2502.03606
  2. Z. Su, Y. Tong, G.-W. Wei. Topology-preserving Hodge Decomposition in the Eulerian Representation. Beijing Journal of Pure and Applied Mathematics , 2 (2025)
    doi:10.4310/BPAM.250908175047, arXiv:2408.14356
  3. Z. Su, Y. Tong, G.-W. Wei. Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning. AIMS Mathematics 9 (2024)
    doi:10.3934/math.20241333, arXiv:2408.00220.
  4. Z. Su, Y. Tong, G.-W. Wei. Hodge decomposition of vector fields in Cartesian grids. SIGGRAPH Asia 2024 Conference Papers (2024)
    https://doi.org/10.1145/3680528.3687602
  5. Z. Su, Y. Tong, G.-W. Wei. Hodge Decomposition of Single-Cell RNA Velocity. Journal of Chemical Information and Modeling (2024)
    doi:10.1021/acs.jcim.4c00132
  6. N. Cavallucci, Z. Su. The metric completion of the space of vector-valued one-forms. Annals of Global Analysis and Geometry 64, 10 (2023)
    doi:10.1007/s10455-023-09916-x , arXiv:2302.06840.
  7. K. Campbell, H. Dai, Z. Su, M. Bauer, T. Fletcher, S. Joshi. Integrated Construction of Multimodal Atlases with Structural Connectomes in the Space of Riemannian Metrics. The Journal of Machine Learning for Biomedical Imaging 1 (2022) doi:10.59275/j.melba.2022-a871, arXiv:2109.09808.
  8. K. Campbell, H. Dai, Z. Su, M. Bauer, T. Fletcher, S. Joshi. Structural Connectome Atlas Construction in the Space of Riemannian Metrics. Information Processing in Medical Imaging 2021 (IPMI 2021)
    doi:10.1007/978-3-030-78191-0_23 , arXiv:2103.05730.
  9. M. Bauer, E. Klassen, S. Preston, Z. Su. A diffeomorphism-invariant metric on the space of vector-valued one-forms. Pure and Applied Mathematics Quarterly, Vol. 17, No. 1 (2021), pp. 141-183.
    doi:10.4310/PAMQ.2021.v17.n1.a4 arXiv:1812.10867.
  10. Z. Su, M. Bauer, E. Klassen, K. Gallivan. Simplifying Transformations for a Family of Elastic Metrics on the Space of Surfaces. 2020 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
    doi:10.1109/CVPRW50498.2020.00432
  11. Z. Su, M. Bauer, S. Preston, H. Laga, E. Klassen. Shape Analysis of Surfaces Using a New Family of Elastic Metrics. Journal of Mathematical Imaging and Vision
    doi:10.1007/s10851-020-00959-4, arXiv:1910.02045, 2019.
  12. Z. Su, M. Bauer, E. Klassen. Comparing Curves in Homogeneous Spaces. Differential Geometry and its Applications, 60 (2018), 9-32.
    doi:10.1016/j.difgeo.2018.05.001, arXiv:1712.04586.
  13. Z. Su, M. Bauer, E. Klassen. The Square Root Velocity Framework for Curves in a Homogeneous Space. 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), (2017) 680–689.
    doi:10.1109/CVPRW.2017.97, arXiv:1706.03095.

Software Packages

  1. A 5-component Hodge decomposition of vector fields in the Cartesian grid. https://github.com/zhesu1/5ComponentHD.
  2. The Helmholtz-Hodge decomposition of vector fields on a bounded domain in a 2d Cartesian grid. https://github.com/zhesu1/HHD.
  3. Surface registration of spherical surfaces with the general elastic metrics. https://github.com/zhesu1/surfaceRegistration.
  4. Geometric shape analysis of spherical surfaces with the first order elastic metrics. https://github.com/zhesu1/elasticMetrics.
  5. Geometric shape analysis of open curves with values in homogeneous spaces. https://github.com/zhesu1/SRVFhomogeneous.

Teaching

Auburn University

Michigan State University

Florida State University