Darrick Lee Postdoctoral Researcher, Oxford applied algebraic topology signature methods
Contact Office: S3.20 Email: darrick.lee at maths.ox.ac.uk

About

I am currently a postdoc in the Mathematical Institute at the University of Oxford as part of the CIMDA-Oxford collaboration with Harald Oberhauser. Previously, I was 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 parametrized data. Currently, most of my work revolves around applications and generalizations of the path signature from a topological and geometric point of view.

Publications and Preprints

  1. Capturing graphs with hypoelliptic diffusions, C. Toth, D. Lee, C. Hacker, and H. Oberhauser
    (accepted in NeurIPS) (2022)
  2. A topological approach to mapping space signatures, C. Giusti, D. Lee, V. Nanda, and H. Oberhauser
    (preprint) (2022)
  3. Signatures, Lipschitz-free spaces, and paths of persistence diagrams, C. Giusti and D. Lee
    (preprint) (2021)
  4. Path signatures on Lie groups, D. Lee and R. Ghrist
    (preprint) (2020)
  5. 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]
  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)
  7. Structure of vortex-bound states in spin singlet chiral superconductors, D. Lee and A. Schnyder
    Physical Review B. 93: 064522 (2016) [arXiv]
  8. 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