Publications

Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. A higher Boltzmann distribution. Accepted for publication
in Journal of Applied and Computational Topology. Available on the arxiv.

Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Exciton Scattering via Algebraic Topology. Accepted for
publication in Journal of Topology and Analysis. Available on the arxiv.

Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting, Chemical Physics, 481, 2016. Available on the arxiv.

Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Stochastic dynamics of extended objects in driven systems II: Current quantization in the low-temperature limit, Chemical Physics, 481, 2016. Available on the arxiv.

Catanzaro, Michael J.; Shi, Tian; Tretiak, Sergei; Chernyak, Vladimir Y. Counting the number of excited states in orgranic semiconductor systems using topology, J. Chem. Phys, 142, 2015. Available on the arxiv.

Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Kirchhoff’s theorems in higher dimensions and Reidemeister torsion, Homology, Homotopy, and Applications, 17, 2015. Available on the arxiv.

Li, Hao; Catanzaro, Michael J.; Tretiak, Sergei; Chernyak, Vladimir. Excited-state structure modifications due to molecular substituents and exciton scattering in conjugated molecules, J. Phys. Chem. Letter, 5, 2014. Available on the arxiv.

Catanzaro, Michael J.; Chernyak, Vladimir Y.; and Klein, John R. On Kirchhoff’s theorems with coefficients in a line bundle, Homology, Homotopy, and Applications, 15, 2013. Available on the arxiv.

Catanzaro, Michael J. Generalized Tonnetze, J. Math. Music, 5, 2011. Available on the arxiv.

Books, In progress

Bruner, Robert R.; Catanzaro, Michael J.; May, J. Peter. Characteristic Classes. pp 97. Draft available at math.uchicago.edu/~may/CHAR/charclasses.pdf.

Theses

Catanzaro, Michael J., “A Topological Study Of Stochastic Dynamics On CW Complexes” (2016). Wayne State University Dissertations. 1433. http://digitalcommons.wayne.edu/oa_dissertations/1433.

Catanzaro, Michael J, “Finitely Presented Modules over the Steenrod Algebra in sage” (2011). Wayne State University Theses. 602. http://digitalcommons.wayne.edu/oa_theses/602/

Expository

The following is an expository paper I wrote on the types of stochastic processes I’m interested in:

Catanzaro, Michael J. A user’s guide: Dynamics and fluctuations of cellular cycles on CW complexes. Available at mathusersguides.com.