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, as well as biological applications. I also have a strong 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
- 18–21 May, 2026: I'm giving a talk at the ICERM Workshop on Foundations of Computational Geometry and Topology in Providence, RI.
Publications
Author order reflects relative contribution, except where authors are marked with an asterisk (*) to indicate equal contribution.
- Persistence Diagram Bundles: A Multidimensional Generalization of Vineyards.
A. Hickok.
Foundations of Computational Mathematics, in press. - Decomposing the Persistent Homology Transform of Star-Shaped Objects.
*S. Arya, *B. Giunti, *A. Hickok, *L. Kanari, *S. McGuire, K. Turner.
Research in Computational Topology 3, Association for Women in Mathematics Series, in press. - Recovering Manifold Structure Using Ollivier-Ricci Curvature.
T. Saidi, A. Hickok, A. J. Blumberg.
Spotlight paper in Proceedings of the International Conference on Learning Representations, 2025. - Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites.
*A. Hickok, *B. Jarman, *M. Johnson, *J. Luo, M. A. Porter.
SIAM Review, 2024. - 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. - 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. - A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs.
A. Hickok, Y. H. Kureh, H. Z. Brooks, M. Feng, M. A. Porter.
SIAM Journal on Applied Dynamical Systems 21(1):1-32, 2022. - 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.
Preprints
- Discrete Scalar Curvature as a Weighted Sum of Ollivier-Ricci Curvatures.
A. Hickok and A. J. Blumberg.
- EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings.
T. Saidi, A. Hickok, B. Rieck, and A. J. Blumberg.
- An Intrinsic Approach to Scalar-Curvature Estimation for Point Clouds.
A. Hickok and A. J. Blumberg.
- Computing Persistence Diagram Bundles.
A. Hickok.
- A Family of Density-Scaled Filtered Complexes.
A. Hickok.
- Math UN1201: Calculus III (Spring 2026)
- 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)
- Math 215: Honors Analysis (Spring 2018)
- Math 335: Complex Analysis (Fall 2017)