Zhe Su

Zhe Su's Picture

Department of Mathematics, Michigan State University, East Lansing
Office: C115, Wells Hall
E-mail: suzhe@msu.edu
URL : https://zhesu1.github.io/

About Me

I am currently a research associate at Michigan State University working with Guowei Wei . Prior to this, I held a postdoc position at the University of California, Los Angeles working with Shantanu Joshi. I finished 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 geometric shape analysis. I aim to develop mathematical frameworks to address interdisciplinary problems in mathematics, data science, medical imaging, and machine learning.

Research Interests

Differential Geometry, Topological and Geometric Data Analysis, Shape Analysis, Data Science, Machine Learning/Deep Learning

Published Articles

  1. Z. Su, Y. Tong, G.-W. Wei. Topology-preserving Hodge Decomposition in the Eulerian Representation. (2024) Beijing Journal of Pure and Applied Mathematics , accepted, (2024)
    arXiv:2408.14356
  2. Z. Su, Y. Tong, G.-W. Wei. Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning. AIMS Mathematics 9 (2024)
    https://doi: 10.3934/math.20241333, arXiv:2408.00220.
  3. 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
  4. Z. Su, Y. Tong, G.-W. Wei. Hodge Decomposition of Single-Cell RNA Velocity. Journal of Chemical Information and Modeling (2024)
    https://doi.org/10.1021/acs.jcim.4c00132
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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
  10. 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.
  11. 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.
  12. 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

Michigan State University

Florida State University