My main areas of research lie within applied and computational mathematics, algebraic topology, and mathematical physics.

Publications

E. Berry, Y.C. Chen,  J. Cisewski-Kehe, and B.T. Fasy. (2020) Functional summaries of persistence diagrams. Accepted for publication in Journal of Applied and Computational Topology. 

E. Berry, R. Nerem, B. Cummins, T. Gedeon, L. Smith, and S. Haase. (2019) Characterizing extremal events in noisy time series. Journal of Mathematical Biology, 1-35.

Recent projects

  • The cohomology of real Grassmannians: We provide a generalization of Morse cohomology to stratified spaces. We investigate this cochain complex for the Schubert stratification of real Grassmannians, and provide a closed formula for the boundary maps in the cochain complex. We provide a number of computations using our framework. For instance, the number of Z/2Z summands in the 72nd homology group of the Grassmannian of 12-planes in 24-dimensional space is 30,525! This is joint work with S. Tiliton, and stemmed from his undergraduate research project that I helped mentor. Check out the preprint (arXiv:2011.07695) or this video for more details!
  • Additivity of factorization algebras: We prove an analog of Dunn's additivity for general factorization algebras. From this, we deduce the additivty of locally constant factorization algebras. Thus, our work is independent of Dunn's additivity, and in particular, specializes to give a new proof of Dunn's additivity.