I am an Assistant Professor of Mathematics at Florida State University. My research is in applications of geometry and topology to problems in data science. My main interests are optimal transport, metric geometry, topological data analysis, and symplectic geometry.
My research is partially supported by NSF grants DMS--2107808 and DMS--2324962 .
For more details, please see my Curriculum Vitae (updated May 2024). Links to my papers are included below.
Equivalence of Landscape and Erosion Distances for Persistence Diagrams. With C. Ayhan. Preprint.
Optimization and the Topology of Spaces of Parseval Frames. With A. Caine and C. Shonkwiler. Preprint.
Robust Representation and Estimation of Barycenters and Modes of Probability Measures on Metric Spaces. With W. Mio, 2025. Preprint.
Stability of Hypergraph Invariants and Transformations. With E. Semrad, 2024. Preprint.
Fused Gromov-Wasserstein Variance Decomposition with Linear Optimal Transport. M. Wilson, T. Needham, and A. Srivastava, 2024. Preprint.
Metric properties of partial and robust Gromov-Wasserstein distances. With J. Chhoa, M. Ivanitskiy, F. Jiang, S. Li, D. McBride, and K. O'Hare, 2024. Preprint.
Geometry of the Space of Partitioned Networks: A Unified Theoretical and Computational Framework. Stephen Zhang, Fangfei Lan, Youjia Zhou, Agnese Barbensi, Michael P. H. Stumpf, Bei Wang and Tom Needham, 2024. Preprint.
The Z-Gromov-Wasserstein Distance. With Martin Bauer, Facundo Mémoli and Mao Nishino, 2024. Preprint.
Geometric Approaches to Matrix Normalization and Graph Balancing. With C. Shonkwiler, 2024. Preprint.
Grassmannian geometry of framed curve spaces. Phd Dissertation, 2016. Preprint
Path constrained unbalanced optimal transport. With M. Bauer, N. Charon and M. Nishino. To appear: Nonlinearity, 2025. Preprint.
Flexible and Probabilistic Topology Tracking with Partial Optimal Transport. M. Li, X. Yan, L. Yan, T. Needham, B. Wang. To appear: IEEE Transactions on Computer Graphics and Visualization, 2025. Preprint.
Topological optimal transport for geometric cycle matching. S. Zhang, M. P. H. Stumpf, T. Needham and A. Barbensi. Journal of Applied and Computational Topology, 2025. Paper. Preprint.
Interleaving Distances, Monoidal Actions and 2-Categories. With P. K. McFaddin. To appear: Algebraic and Geometric Topology, 2025. Preprint.
Cortical Coding of Gustatory and Thermal Signals in Active Licking Mice. A. N. Nash, C. G. Bouaichi, K. E. Odegaard, T. Needham, M. Bauer, R. Bertram, R. Vincis. To appear: Journal of Physiology. Preprint.
Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distances. With R. A. Clark and T. Weighill. To appear: AAAI 2025. Preprint.
On the Existence of Parseval Frames for Vector Bundles. With S. A. Ballas and C. Shonkwiler. To appear: Transactions of the AMS, 2025. Preprint.
Comparison Results for Gromov-Wasserstein and Gromov-Monge Distances. With F. Mémoli. ESAIM: Control, Optimization and Calculus of Variations, 2024. Article. Preprint.
Statistical Analysis of Complex Shape Graphs. A. Basu Bal, X. Guo, T. Needham, A. Srivastava. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024. Preprint. Article.
A Wasserstein-type Distance for Gaussian Mixtures on Vector Bundles with Applications to Shape Analysis. M. Wilson, T. Needham, C. Park, S. Kundu, A. Srivastava. Accepted to SIAM Journal on Imaging Sciences, 2024. Preprint.
Elastic Metrics on Spaces of Euclidean Curves: Theory and Algorithms. With M. Bauer, N. Charon, E. Klassen, S. Kurtek, T. Pierron. Journal of Nonlinear Science, 2024. Article. Preprint.
Stability and Approximations for Decorated Reeb Spaces. With J. Curry, W. Mio, O. B. Okutan and F. Russold. Accepted to Symposium on Computational Geometry, 2024. Article. Preprint.
Convergence of Leray Cosheaves for Decorated Mapper Graphs. With J. Curry, W. Mio, B. Okutan, F. Russold, 2023. Presented as an extended abstract at Young Researchers Forum (YRF) of the 39th International Symposium on Computational Geometry (SoCG 2023). Preprint.
Comparing Morse Complexes Using Optimal Transport: An Experimental Study. With M. Li, C. Storm, A. Y. Li and B. Wang. Accepted to IEEE Visualization Conference, Short Paper, 2023. Preprint.
Topologically Attributed Graphs for Shape Discrimination. With J. Curry, W. Mio, B. Okutan, F. Russold, 2023. Accepted to ICML Workshop Topology, Algebra and Geometry in Machine Learing, 2023. Preprint.
Hypergraph Co-Optimal Transport: Metric and Categorical Properties. With S. Chowdhury, E. Semrad, B. Wang, Y. Zhou. To Appear: Journal of Applied and Computational Topology, 2023. Preprint.
Gromov-Wasserstein Distances, Distance Distributions and Inverse Problems for Metric Measure Spaces. With F. Mémoli. Oberwolfach Reports, 2023. Article.
Fusion Frame Homotopy and Tightening Fusion Frames by Gradient Descent. With C. Shonkwiler. Preprint. Accepted to Journal of Fourier Analysis and Applications, 2023.
Three proofs of the Benedetto-Fickus theorem. With D. Mixon, C. Shonkwiler, S. Villar. Chapter in: Sampling, Approximation, and Signal Analysis, 2024. Article. Preprint.
Geometric averages of partitioned datasets. With T. Weighill. SIAM Journal on Applied Algebra and Geometry, 2023. Article. Preprint.
Active licking shapes cortical taste coding. C. Neese, C. G. Bouaichi, T. Needham, M. Bauer, R. Bertram and R. Vincis. The Journal of Neuroscience. Article. Preprint.
Distance distributions and inverse problems for metric measure spaces. With F. Mémoli. Studies in Applied Mathematics, 2022. Preprint. Article.
Toric Symplectic Geometry and Full Spark Frames. With C. Shonkwiler, 2021. Applied and Computational Harmonic Analysis, 2022. Preprint. Article.
Admissibility and Frame Homotopy for Quaternionic Frames. With C. Shonkwiler. Linear Algebra and Its Applications, 2022. Preprint. Article.
Decorated Merge Trees for Persistent Topology. With J. Curry, H. Hang, W. Mio and O. Okutan. Journal of Applied and Comptutational Topology, 2022. Preprint. Article.
Statistical shape analysis of brain arterial networks. With X. Guo, A. Basu Bal and A. Srivastava. Annals of Applied Statistics, 2021. Preprint.
Quantized Gromov-Wasserstein. With S. Chowdhury and D. Miller, 2021. Proceedings of ECML 2021. Preprint.
Generalized Spectral Clustering via Gromov-Wasserstein Learning. With S. Chowdhury. Proceedings of AISTATS 2021. Article. Preprint.
The (homological) persistence of gerrymandering. With M. Duchin and T. Weighill. Foundations of Data Science, 2021. Article. Preprint.
Symplectic geometry and connectivity of spaces of frames. With C. Shonkwiler. Advances in Computational Mathematics, 2021. Article. Preprint.
Gromov-Wasserstein Averaging in a Riemannian Framework. With S. Chowdhury. CVPR workshop DIFF-CVML proceedings, 2020. Preprint.
The Weighted Euler Curve Transform for Shape and Image Analysis. With Q. Jiang and S. Kurtek. CVPR workshop DIFF-CVML proceedings, 2020. Preprint.
Simplifying transforms for general elastic metrics on the space of plane curves. With S. Kurtek. SIAM Journal on Imaging Sciences, 2020. Article. Preprint.
Knot types of generalized Kirchhoff rods. Journal of Knot Theory and its Ramifications, 2019. Preprint. Article.
Random triangles and polygons in the plane. With J. Cantarella, C. Shonkwiler and G. Stewart. American Mathematical Monthly, 2019. Article. Preprint.
Shape analysis of framed space curves. Journal of Mathematical Imaging and Vision, 2019. Preprint.
The Paulsen problem made symplectic. With M. Ehler, M. Hering, C. Manon and C. Shonkwiler. Oberwolfach Reports, 2018. Proceedings.
Symplectic Geometry and Frame Theory. With C. Shonkwiler. Oberwolfach Reports, 2018. Proceedings.
Kahler structures on spaces of framed curves. Annals of Global Analysis and Geometry, 2018. Article. Preprint.
Sparse recovery from saturated measurements. With S. Foucart. Information and Inference, 2016. Article.
Sparse disjointed recovery from noninflating measurements. With S. Foucart and M. Minner. Applied and Computational Harmonic Analysis, 2015. Article.
Dictionary-sparse and disjointed recovery. In: Proceedings of Sampling Theory and Applications 11th Annual Conference, 2015. Article.