Research


Here is my Google Scholar Page.

Preprints

  • Random Walks, Conductance, and Resistance for the Connection Graph Laplacian (With Alexander Cloninger, Gal Mishne, Andreas Oslandsbotn, Sawyer Jack Robertson, Yusu Wang.) arXiv preprint arXiv:2308.09690 (2023). Code
  • Distances for Markov Chains, and Their Differentiation (With Tristan Brugère, Yusu Wang.) arXiv preprint arXiv:2302.08621 (2023).
  • Some results about the Tight Span of spheres (With Sunhyuk Lim, Facundo Mémoli, Qingsong Wang, Ling Zhou.) arXiv preprint arXiv:2112.12646 (2021).
  • The Gaussian transform (With Kun Jin, Facundo Mémoli.) arXiv preprint arXiv:2006.11698 (2020).

    • Journal papers

  • The ultrametric Gromov-Wasserstein distance (With Facundo Mémoli, Axel Munk, Christoph Weitkamp.) To appear in Discrete & Computational Geometry. arXiv preprint arXiv:2101.05756 (2023). Code
  • Characterization of Gromov-type geodesics (With Facundo Mémoli.) Differential Geometry and its Applications, 88:102006 (2023).
  • The Gromov-Hausdorff distance between ultrametric spaces: its structure and computation (With Facundo Mémoli, Zane Smith.) To appear in Journal of Computational Geometry. arXiv preprint arXiv:2110.03136 (2023). Code Video
  • On p-metric spaces and the p-Gromov-Hausdorff distance (With Facundo Mémoli.) p-Adic Numbers, Ultrametric Analysis and Applications, 14, pages 173–223 (2022).
  • Persistent Laplacians: properties, algorithms and implications (With Facundo Mémoli, Yusu Wang.) SIAM Journal on Mathematics of Data Science, 4(2):858–884, 2022. Code
  • A novel construction of Urysohn universal ultrametric space via the Gromov-Hausdorff ultrametric Topology and its Applications, 300:107759, 2021.

    • Conference papers

  • The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs (With Samantha Chen, Sunhyuk Lim, Facundo Mémoli, Yusu Wang.) ICML workshop: Topology, Algebra, and Geometry in Machine Learning (2023).
  • The Persistent Laplacian for Data Science: Evaluating Higher-Order Persistent Spectral Representations of Data (With Thomas Davies, Ruben Sanchez-Garcia.) International Conference on Machine Learning (ICML 2023).
  • Understanding Oversquashing in GNNs through the Lens of Effective Resistance (With Mitchell Black, Amir Nayyeri, Yusu Wang.) International Conference on Machine Learning (ICML 2023). Code
  • The Numerical Stability of Hyperbolic Representation Learning (With Gal Mishne, Yusu Wang, Sheng Yang.) International Conference on Machine Learning (ICML 2023). Code
  • A generalization of the persistent Laplacian to simplicial maps (With Aziz Burak Gülen, Facundo Mémoli, Yusu Wang.) 39th International Symposium on Computational Geometry (SoCG 2023).
  • Weisfeiler-Lehman meets Gromov-Wasserstein (With Samantha Chen, Sunhyuk Lim, Facundo Mémoli, Yusu Wang.) International Conference on Machine Learning (ICML 2022). Code Video
  • The Wasserstein transform (With Facundo Mémoli, Zane Smith.) International Conference on Machine Learning (ICML 2019).

    • PhD Thesis

  • Distances within and between Metric Spaces: Metric Geometry, Optimal Transport and Applications to Data Analysis