About

I am currently a Chancellor’s Fellow in the School of Mathematics at the University of Edinburgh. Previously, I was a postdoc in the Mathematical Institute at the University of Oxford as part of the CIMDA-Oxford collaboration with Harald Oberhauser and a postdoc in the Laboratory for Topology and Neuroscience at EPFL with Kathryn Hess. I received my PhD in Applied Mathematics and Computational Sciences (AMCS) in 2021 at the University of Pennsylvania working under Rob Ghrist. Before that, I received my Bachelor of Applied Sciences at the University of British Columbia in 2016, where I majored in Engineering Physics with an Electrical Engineering specialization and minored in Mathematics.

I received a Fulbright Canada student award for 2016-2017 and a NSERC PGS-D scholarship for 2018-2021.

My CV is here.

Research

I am interested in developing mathematics at the interface of topology, geometry, and analysis in order to build novel tools to study functional data. Currently, most of my work revolves around applications and generalizations of the path signature from a topological and geometric point of view.

I am co-organizing the Applied Geometry, Algebra, and Topology in Edinburgh (AGATE) seminar with Djordje Mihajlovic and Siddharth Setlur.

I am co-organizing the North British Probability Seminar with Theo Assiotis.

Past Events:

• With Gonçalo dos Reis and Yue Wu, I co-organized the ICMS Workshop Signatures and Rough Paths: From Stochastics, Geometry and Algebra to Machine Learning from May 19-23, 2025.
• During Summer 2025, I co-organized a learning seminar on Hodge Theory for Cellular and Network Sheaves with Yusuf Bariş Kartal.

Preprints

1. Orthogonal polynomials on path-space, I. Chevyrev, E. Ferruci, D. Lee, T. Lyons, H. Oberhauser, N. Tapia
   (preprint) (2026)
2. Thin homotopy and the signature of piecewise linear surfaces, F. Bischoff, D. Lee
   (preprint) (2025)
3. Path-dependent SDEs: solutions and parameter estimation, P. Semnani, V. Guan, E. Robeva, D. Lee
   (preprint) (2025)
4. The surface signature and rough surfaces, D. Lee
   (preprint) (2024)
5. Random surfaces and higher algebra, D. Lee and H. Oberhauser
   (preprint) (2023)
6. Path signatures on Lie groups, D. Lee and R. Ghrist
   (preprint) (2020)
7. A methodology for morphological feature extraction and unsupervised cell classification. D. Bhaskar, D. Lee, H. Knútsdóttir, C. Tan, M. Zhang, P. Dean, C. Roskelley, and L. Edelstein- Keshet
   (preprint) (2019)

Journal / Conference Publications

* equal contribution

1. Communities in the Kuramoto model: dynamics and detection via path signatures, T. J. Nguyên, D. Lee, B. J. Stolz
   Journal of Physics: Complexity, Focus Issue on Higher Order Brain Networks (2025) [arXiv]
2. Ergodic trajectory optimization on generalized domains using maximum mean discrepancy, C. Hughes, H. Warren, D. Lee, F. Ramos, I. Abraham
   IEEE International Conference on Robotics and Automation (ICRA) (2025) [arXiv]
3. Towards scalable topological regularizers, H.-T. Wong*, D. Lee*, H. Yan
   International Conference on Learning Representations (ICLR) (2025) [arXiv]
4. Generalized time series classification via component decomposition and alignment, Y. Cheng, D. Lee, H. Oberhauser, H. Li
   IEEE Transactions on Big Data. (2025)
5. A topological approach to mapping space signatures, C. Giusti, D. Lee, V. Nanda, and H. Oberhauser
   Advances in Applied Mathematics. (2025) [arXiv]
6. Stein variational ergodic search, D. Lee, C. Lerch, F. Ramos, I. Abraham
   Robotics: Science and Systems (2024)
7. Signatures, Lipschitz-free spaces, and paths of persistence diagrams, C. Giusti and D. Lee
   SIAM Journal on Applied Algebra and Geometry. (2023) [arXiv]
8. Signature methods for brain-computer interfaces, X. Xu, D. Lee, N. Drougard, and R. N. Roy
   Scientific Reports. (2023)
9. Convex hulls of curves: volumes and signatures, C. Améndola, D. Lee, and C. Meroni
   In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. (2023) [arXiv]
10. Capturing graphs with hypoelliptic diffusions, C. Toth*, D. Lee*, C. Hacker, and H. Oberhauser
    Advances in Neural Information Processing Systems (NeurIPS) (2022) [arXiv]
11. Structure of vortex-bound states in spin singlet chiral superconductors, D. Lee and A. Schnyder
    Physical Review B. 93: 064522 (2016) [arXiv]
12. Localization for transversally periodic random potentials on binary trees, R. Froese, D. Lee, C. Sadel, W. Spitzer, and G. Stolz
    Journal of Spectral Theory. 6: 557-600 (2016) [arXiv]

Book Chapters

1. The signature kernel, D. Lee and H. Oberhauser
   In C. Bayer, G. dos Reis, B. Horvath, H. Oberhauser, editors, Signature Methods in Finance, Springer Finance, pages 85-124 (2025) [arXiv]
2. Iterated integrals and population time series analysis, C. Giusti and D. Lee
   In N. Baas, G. Carlsson, G. Quick, M. Szymik, and M. Thaule, editors, Topological Data Analysis, Abel Symposia, pages 219–246 (2020) [arXiv]

Teaching

University of Edinburgh

• Winter 2026 Course Organizer for MATH 10003: Financial Mathematics

EPFL

• Fall 2021 TA for MATH 220: Metric and Topological Spaces

University of Pennsylvania

• August 2020 Co-Instructor for Pre-Freshman Program
• Spring 2018 TA for MATH 241: Calculus IV (Partial Differential Equations)
• Fall 2017 TA for MATH 360: Advanced Calculus (Real Analysis)
  Math Department Good Teaching Award