Research


Here is my Google Scholar Page.

Preprints

  • All You Need is Resistance: On the Equivalence of Effective Resistance and Certain Optimal Transport Problems on Graphs (With Sawyer Robertson, Alexander Cloninger.) arXiv preprint arXiv:2404.15261 (2024).
  • Orthogonal Möbius Inversion and Grassmannian Persistence Diagrams (With Aziz Burak Gülen, Facundo Mémoli.) arXiv preprint arXiv:2311.06870 (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

  • Random Walks, Conductance, and Resistance for the Connection Graph Laplacian (With Alexander Cloninger, Gal Mishne, Andreas Oslandsbotn, Sawyer Jack Robertson, Yusu Wang.) To appear in SIAM Journal on Matrix Analysis and Applications (SIMAX). Code
  • 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

  • Comparing Graph Transformers via Positional Encodings (With Mitchell Black, Gal Mishne, Amir Nayyeri, Yusu Wang.) To appear in International Conference on Machine Learning (ICML 2024).
  • Distances for Markov Chains, and Their Differentiation (With Tristan Brugère, Yusu Wang.) International Conference on Algorithmic Learning Theory (ALT 2024).
  • 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