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

My google scholar page

Exploring moduli spaces of Morse functions

  • 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. Available on the arXiv at arXiv:1909.10623. Published in the Journal of Applied and Computational Topology. Available through Springer.

  • Catanzaro, Michael J.; Wang, Bei; Zabka, Matthew; Zhou, Youjia. MVF Designer: Design and Visualization of Morse Vector Fields. Available on the arXiv at arXiv:1912.09580. Submitted.

Random chain complexes

  • Catanzaro, Michael J.; Zabka, Matthew J. A Model for Random Chain Complexes. Available on the arXiv at arXiv:1901.00964. Submitted.

Stochastic Currents and Markov CW chains

Exciton Scattering

Topology and music theory

Theses

Expository

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