Research Experience

RESEARCH EXPERIENCE

My graduate research area is persistent homology, which is a field within Topological Data Analysis. I study the mathematical foundations of persistent homology using techniques from commutative algebra and quiver representation theory. My work focuses on the relationships between invariants of persistence modules as well as the structure of indecomposable persistence modules.

My advisor is Dr. Richárd Rimányi. I am also thank to Dr. Ezra Miller at Duke, who has welcomed me into his research group.

My graduate research has been supported by a National Science Foundation Graduate Research Fellowship under Grant No. 1650116.

As an undergraduate, I completed three other research projects. The first was an REU at Grand Valley State University in summer 2015. There I worked under Dr. William Dickinson with another undergraduate, Robert Dickens, to study maximally dense circle packings on Klein bottles. In summer 2016 I completed a second REU at Texas A&M University, where I worked under Dr. Matthew Young to study an analytic number theory problem, namely finding the zeros of an Eisenstein series. In the 2016-2017 school year, I also worked on a McNair Scholars Research Project at University of Northern Colorado.My advisor was Dr. Katherine Morrison, and we studied a mathematical model of neural networks.

PUBLICATIONS AND MANUSCRIPTS

(5) W. Kim and S. Moore. The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers. arXiv:2111.02551. Preprint. 2021.
arXiv version
(4) S. Moore. Hyperplane Restrictions of Indecomposable n-Dimensional Persistence Modules. To appear in Homology, Homotopy, and Applications. 2021.
arXiv version
(3) S. Moore. A combinatorial Formula for the Bigraded Betti Numbers. arXiv:2004.02239. Manuscript. 2021.
arXiv version
(2) C. Parmelee, S. Moore, K. Morrison, C. Curto. Core motifs predict dynamic attractors in combinatorial threshold-linear networks. arXiv:2109.03198. Preprint. 2021.
arXiv version
(1) S. Moore. On the Zeroes of Half-Integral Weight Eisenstein Series on Γ₀(4). International Journal of Number Theory. 2019.
arXiv version

PRESENTATIONS

Invited Talks (15) The generalized persistence diagram encodes the bigraded Betti numbers. Applied Algebraic Topology Research Network Seminar, July 2022. (14) The generalized persistence diagram encodes the bigraded Betti numbers. AMS Southeastern Sectional Meeting, March 2022. (13) Hyperplane restrictions of n-parameter persistence modules. AMS Southeastern Sectional Meeting, March 2022. (12) Hyperplane restrictions of n-parameter persistence modules. University of Florida Topological Data Analysis Meeting, January 2022. Contributed Talks (11) Hyperplane restrictions of n-dimensional persistence modules. Joint Math Meetings, January 2022. (10) Hyperplane restrictions of n-dimensional persistence modules. SIAM Conference on Applied Algebraic Geometry, August 2021. (9) Girls Talk Math: Engaging high school girls in college-level mathematics. Launch Point (a local conference in North Carolina), April 2021 (8) Hyperplane restrictions of n-dimensional persistence modules. Triangle Area Graduate Mathematics Conference (a local conference in North Carolina), December 2020. (7) Persistent Homology. UNC-Chapel Hill Graduate Mathematics Association Seminar, October 2019. (6) Predicting network dynamics based on neural connectivity. 23rd Annual Undergraduate Research Conference at SUNY Buffalo, July 2017. (5) Predicting network dynamics based on neural connectivity. University of Northern Colorado Math Club Seminar, April 2017. (4) Predicting network dynamics based on neural connectivity. Nebraska Conference for Undergraduate Women, January 2017. (3) Packing three equal circles on a flat Klein bottle. Joint Math Meetings, January 2016. (2) Packing three equal circles on a flat Klein bottle. MAA Mathfest, August 2015.       Awarded the MAA Outstanding Presentation Award (1) Packing three equal circles on a flat Klein bottle. SUMMR (a local conference in Michigan), July 2015.

MENTORSHIP

In Summer 2017, I mentored a female high school student learning about non-Euclidean geometry at the Frontiers of Science Institute, which is held at the University of Northern Colorado. This project was completed via Inquiry-Based Learning.
In Spring 2020, I mentored an undergraduate Latina student through the Directed Reading Program at the University of North Carolina at Chapel Hill. She was reading about elementary number theory and cryptography.