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.

For 2024-2025, Sjoerd Beentjes, Emily Roff and I are organizing the Applied Geometry, Algebra, and Topology in Edinburgh (AGATE) seminar.

Preprints

1. Ergodic trajectory optimization on generalized domains using maximum mean discrepancy, C. Hughes, H. Warren, D. Lee, F. Ramos, I. Abraham
   (preprint) (2024)
2. The surface signature and rough surfaces, D. Lee
   (preprint) (2024)
3. Random surfaces and higher algebra, D. Lee and H. Oberhauser
   (preprint) (2023)
4. The signature kernel, D. Lee and H. Oberhauser
   (preprint of book chapter) (2023)
5. Path signatures on Lie groups, D. Lee and R. Ghrist
   (preprint) (2020)
6. 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)

Publications

1. A topological approach to mapping space signatures, C. Giusti, D. Lee, V. Nanda, and H. Oberhauser
   Advances in Applied Mathematics. (2025) [arXiv]
2. Stein variational ergodic search, D. Lee, C. Lerch, F. Ramos, I. Abraham
   Robotics: Science and Systems (2024)
3. Signatures, Lipschitz-free spaces, and paths of persistence diagrams, C. Giusti and D. Lee
   SIAM Journal on Applied Algebra and Geometry. (2023) [arXiv]
4. Signature methods for brain-computer interfaces, X. Xu, D. Lee, N. Drougard, and R. N. Roy
   Scientific Reports. (2023)
5. 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]
6. Capturing graphs with hypoelliptic diffusions, C. Toth, D. Lee, C. Hacker, and H. Oberhauser
   Advances in Neural Information Processing Systems (NeurIPS) (2022) [arXiv]
7. Iterated integrals and population time series analysis, C. Giusti and D. Lee
   In Nils A. Baas, Gunnar E. Carlsson, Gereon Quick, Markus Szymik, and Marius Thaule, editors, Topological Data Analysis, Abel Symposia, pages 219–246 (2020) [arXiv]
8. Structure of vortex-bound states in spin singlet chiral superconductors, D. Lee and A. Schnyder
   Physical Review B. 93: 064522 (2016) [arXiv]
9. 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]

Teaching

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