Here is a list of submitted manuscripts and published articles I have worked on.

My google scholar page

Topological data analysis

  • Catanzaro, Michael J.; Rizzo, Sam; Kopchick, John; Chodury, Asadur; Rosenberg, David R.; Bubenik, Peter; Diwadkar, Vaibhav A. Topological Data Analysis Captures Task-Driven fMRI Profiles in Individual Participants: A Classification Pipeline Based on Persistence, Neuroinformatics. (2023), DOI

  • Smith, Abraham D.; Catanzaro, Michael J.; Angeloro, Gabrielle; Patel, Nirav; Bendich, Paul. Topological Parallax: A Geometric Specification for Deep Perception Models, Accepted to Neurips 2023. Available on the arXiv at

  • Catanzaro, Michael J.; Przybylski, Lee; Weber, Eric S. Persistence Landscapes of Affine Fractals. Demonstratio Mathematica, 55 (2022), 163–192. Available on the arXiv at arXiv:2201.02552.

  • Catanzaro, Michael J.; Vose, Brantley. Harmonic Representatives in homology over arbitrary fields, J Appl. and Comput. Topology. 7 (2023), 643–670, DOI Available on the arXiv at

Multiparameter persistence

  • Bubenik, Peter; Catanzaro, Michael J. Multiparameter persistent homology via generalized Morse theory. Available on the arXiv at arXiv:2107.08856. Accepted to Fields Institute Communications.

Exploring moduli spaces of Morse functions

  • Zhou, Youjia; Lazovskis, Janis; Catanzaro, Michael J.; Zabka, Matthew; Wang, Bei. Combinatorial Exploration of Morse–Smale Functions on the Sphere via Interactive Visualization. Accepted to IEEE Workshop on Topological Data Analysis and Visualization 2023.
  • Catanzaro, Michael J.; Curry, Justin; Fasy, Brittany Terese; Lazovskis, Janis; Malen, Greg; Riess, Hans; Wang, Bei; Zabka, Matthew. Moduli Spaces of Morse Functions for Persistence. Journal of Applied and Computational Topology, 4 (2020), 353–385. Available on the arXiv at arXiv:1909.10623.

Random chain complexes

Stochastic Currents and Markov CW chains

Exciton Scattering

Topology and music theory



The following is an expository paper I wrote explaining the types of stochastic processes I am interested in studying.