Abigail Hickok


Columbia Department of Mathematics
Email: aghickok (at) gmail (dot) com
Bitbucket

I'm an NSF postdoc fellow at Columbia University, supervised by Andrew Blumberg. I finished my PhD at UCLA in 2023, advised by Mason Porter. Prior to UCLA, I was an undergraduate in the Princeton math department. Here is my CV.

In my research, I focus primarily on topological and geometric data analysis, and I sometimes use tools from computational geometry as well. I also have an interest in network science, especially opinion dynamics and network geometry.

Outside of math, I enjoy rock climbing, running, and playing and composing for piano.

Upcoming talks and travel

Publications and preprints

  1. An Intrinsic Approach to Scalar-Curvature Estimation for Point Clouds.

    A. Hickok and A. J. Blumberg.
    Preprint, 2023.

  2. Computing Persistence Diagram Bundles.

    A. Hickok.
    Preprint, 2022.

  3. Persistence Diagram Bundles: A Multidimensional Generalization of Vineyards.

    A. Hickok.
    Preprint, 2022.

  4. Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites.

    *A. Hickok, *B. Jarman, *M. Johnson, *J. Luo, M. A. Porter.
    Preprint, 2022.

  5. A Family of Density-Scaled Filtered Complexes.

    A. Hickok.
    Preprint, 2022.

  6. Analysis of Spatial and Spatiotemporal Anomalies Using Persistent Homology: Case Studies with COVID-19 Data.

    A. Hickok, D. Needell, M. A. Porter.
    SIAM Journal on Mathematics of Data Science, 4(3):1116-1144, 2022.

  7. Topological Data Analysis of Spatial Systems.

    M. Feng, A. Hickok, M. A. Porter.
    In F. Battiston and G. Petri (eds.) Higher-Order Systems, ch. 17, pp. 389–399. Springer, Cham, Switzerland, 2022.

  8. A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs.

    A. Hickok, Y. Kureh, H. Z. Brooks, M. Feng, M. A. Porter.
    SIAM Journal on Applied Dynamical Systems 21(1):1-32, 2022.

  9. Adaptive Spectral Solution Method for the Landau and Lenard-Balescu Equations.

    C. R. Scullard, *A. Hickok, *J. O. Sotiris, *B. M. Tzolova, *R. L. Van Heyningen, F. R. Graziani.
    Journal of Computational Physics 402, 109110, 2020.

*Equal contribution

Teaching

UCLA (Teaching Assistant):
  • Math 168: Introduction to Networks (Winter 2020, Spring 2020, Fall 2020)
  • Math 31B: Integration and Infinite Series (Winter 2020, Spring 2020)
  • Math 131AH: Honors Analysis (Fall 2019)
  • Math 1: Precalculus (Fall 2019)
Princeton (Undergraduate Course Assistant):
  • Math 215: Honors Analysis (Spring 2018)
  • Math 335: Complex Analysis (Fall 2017)
Plain Academic