My current research interests include topology, continuum theory, and dynamical systems. My focus for the past few years has been on generalized inverse limits of sequences upper semicontinuous set-valued functions on [0,1]. Specifically, we have developed notions of the Intermediate Value Property for usc upper-semicontinuous functions that imply the connectedness of the inverse limit. We have also investigated the relationship between the dynamical properties of an upper semicontinuous function and existence of indecomposable subcontinua of the corresponding inverse limit.
Periodicity and Indecomposability in Generalized Inverse Limits, with David J. Ryden, under review https://arxiv.org/abs/2108.04959v1
A Hereditarily Decomposable Generalized Limit on [0,1] with Periodic Cycles of all Periods, https://arxiv.org/abs/2209.05357
Connected Generalized Inverse Limits and Intermediate Value Property, Topology Proceedings Vol. 60 (2022) pp. 105-117 arXiv:2010.04198