My research is in the area of applied topology or topological data analysis (TDA). My recent work has established the homotopy types of the Vietoris-Rips metric thickenings of the circle [1]. My master's thesis [9] provided the first proof of the stability of persistent homology for Vietoris-Rips and Čech metric thickenings. Extensions of this result will be in an upcoming paper; a preprint [4] is available. My advisor, Henry Adams, and I wrote a paper [6] surveying applications of TDA, focusing on those related to machine learning.
My NASA internships during the summers of 2020, 2021, and 2022 included projects focused on applications of sheaves to networking; see [3],[5],[7],[10]. My internships also included work that improved an algorithm for routing in space called Contact Graph Routing, leading the incorporation of this technique into NASA's HDTN project [2],[11].
Papers and preprints
[1]
Vietoris-Rips Metric Thickenings of the Circle
Available on arXiv
[Link]
[2]
A survey of mathematical structures for lunar networks
With coauthors R. Short, A. Hylton, J. Cleveland, O. Freides, Z. Memon, R. Cardona, R. Green, J. Curry, S. Gopalakrishnan, D. V. Dabke, B. Story, and B. Mallery.
Published at the 2022 IEEE Aerospace Conference.
[Link]
[3]
Sheaf theoretic models for routing in delay tolerant networks
With coauthors R. Short, A. Hylton, J. Cleveland, R. Cardona, R. Green, J. Curry, B. Mallery, G. Bainbridge, and Z. Memon.
Published at the 2022 IEEE Aerospace Conference
[Link]
[4]
The Persistent Topology of Optimal Transport Based Metric Thickenings
With Henry Adams, Facundo Mémoli, and Qingsong Wang.
Accepted to be published in a journal; arXiv preprint available.
[Link]
[5]
Towards sheaf theoretic analyses for delay tolerant networking
With Robert Short, Alan Hylton, Robert Cardona, Robert Green, Gabriel Bainbridge, and Jacob Cleveland. Published in 2021 IEEE Aerospace Conference Proceedings, June 2021.
[Link]
[6]
Topology applied to machine learning: From global to local
With Henry Adams.
Published in Frontiers in Artificial Intelligence, May 2021.
[Link]
[7]
Path Optimization Sheaves
With Robert Cardona, Robert Green, Jacob Cleveland, Alan Hylton, and Robert Short.
Placed on arXiv, Dec. 2020.
[Link]
[8]
Interpreting a topological measure of complexity for decision boundaries
With Alan Hylton, Ian Lim, and Robert Short.
Presented by Ian Lim at ASMDA 2021, to be published in the conference proceedings.
[Conference website]
Thesis
[9]
Persistence stability for metric thickenings
MS thesis, defended March 2021, published by ProQuest July 2021.
[Link]
In Progress
[10]
On the current state of sheaf theoretic networking
With R. Short, J. Cleveland, and Z. Cooperband.
Accepted for publication at the 2022 IEEE WiSEE conference.
[Conference website]
[11]
Contact multigraph routing: overview and implementation
With R. Short, J. Cleveland, Y. Kirkpatrick, and D. Conricode.
Abstract accepted to the 2023 IEEE Aerospace Conference.
[Conference website]
My NASA internships during the summers of 2020, 2021, and 2022 included projects focused on applications of sheaves to networking; see [3],[5],[7],[10]. My internships also included work that improved an algorithm for routing in space called Contact Graph Routing, leading the incorporation of this technique into NASA's HDTN project [2],[11].
Papers and preprints
[1]
Vietoris-Rips Metric Thickenings of the Circle
Available on arXiv
[Link]
[2]
A survey of mathematical structures for lunar networks
With coauthors R. Short, A. Hylton, J. Cleveland, O. Freides, Z. Memon, R. Cardona, R. Green, J. Curry, S. Gopalakrishnan, D. V. Dabke, B. Story, and B. Mallery.
Published at the 2022 IEEE Aerospace Conference.
[Link]
[3]
Sheaf theoretic models for routing in delay tolerant networks
With coauthors R. Short, A. Hylton, J. Cleveland, R. Cardona, R. Green, J. Curry, B. Mallery, G. Bainbridge, and Z. Memon.
Published at the 2022 IEEE Aerospace Conference
[Link]
[4]
The Persistent Topology of Optimal Transport Based Metric Thickenings
With Henry Adams, Facundo Mémoli, and Qingsong Wang.
Accepted to be published in a journal; arXiv preprint available.
[Link]
[5]
Towards sheaf theoretic analyses for delay tolerant networking
With Robert Short, Alan Hylton, Robert Cardona, Robert Green, Gabriel Bainbridge, and Jacob Cleveland. Published in 2021 IEEE Aerospace Conference Proceedings, June 2021.
[Link]
[6]
Topology applied to machine learning: From global to local
With Henry Adams.
Published in Frontiers in Artificial Intelligence, May 2021.
[Link]
[7]
Path Optimization Sheaves
With Robert Cardona, Robert Green, Jacob Cleveland, Alan Hylton, and Robert Short.
Placed on arXiv, Dec. 2020.
[Link]
[8]
Interpreting a topological measure of complexity for decision boundaries
With Alan Hylton, Ian Lim, and Robert Short.
Presented by Ian Lim at ASMDA 2021, to be published in the conference proceedings.
[Conference website]
Thesis
[9]
Persistence stability for metric thickenings
MS thesis, defended March 2021, published by ProQuest July 2021.
[Link]
In Progress
[10]
On the current state of sheaf theoretic networking
With R. Short, J. Cleveland, and Z. Cooperband.
Accepted for publication at the 2022 IEEE WiSEE conference.
[Conference website]
[11]
Contact multigraph routing: overview and implementation
With R. Short, J. Cleveland, Y. Kirkpatrick, and D. Conricode.
Abstract accepted to the 2023 IEEE Aerospace Conference.
[Conference website]