I am interested in multiparameter persistent homology from an algebraic-combinatorial point of view. Many concepts in persistent homology can be unified and simplified by phrasing them in the language of algebraic combinatorics. See here for more details.
Preprints:
A. Burak Gülen and A. McCleary. Galois Connections in Persistent Homology. October 2022.
Published Papers:
A. McCleary and A. Patel.
Edit Distance and Persistence Diagrams Over Lattices.
ArXiv version.
In the SIAM Journal on Applied Algebra and Geometry, July 2022.
A. McCleary and A. Patel.
Bottleneck Stability for Generalized Persistence Diagrams.
ArXiv version.
In the journal Proceedings of the AMS, Volume 148, Number 7, July 2020, pp 3149-3161.
M. Aldi and A. McCleary.
Darboux Calculus.
ArXiv version.
In the journal Involve, Volume 12, Number 3, 2019, pp 361-380.
T. Chomko, K. McCall, A. McCleary, J. Shive, and D. Taylor.
Ring Dominating Functions in Graph Products.
In the journal Bulletin of the Institute of Combinatorics and its Applications.