I am a faculty member of the math department at Creighton University. Previously, I was a postdoctoral fellow of the National Library of Medicine Biomedical Informatics Training Program in the laboratory for the algorithm brain at Baylor College of Medicine. I defended my PhD in combinatorics and discrete geometry with applications to neuroscience at Penn State in 2019. In addition to my academic interests, I enjoy using mathematics as a tool for creating beautiful sculptures.
Broadly speaking, I am interested in how the brain encodes and processes information, with particular focus on the role of receptive field geometry and network connectivity in shaping these properties.
I study the connectome, the "wiring diagram" of the brain, to understand how brain areas interact and encode sensory signals. Using graph theory and discrete geometry, I seek to understand how specific wiring patterns give rise to the receptive field properties observed in many sensory systems.
I study the relationship between the geometry of sets covering a space and their intersection patterns, using tools from combinatorial commutative algebra and algebraic topology.
The questions I think about arise from neuroscience. In many sensory systems, a given neuron will fire actively in response to a certain set of stimuli and remain silent in response to all others. This gives us our cover (the sets of stimuli that drive individual neurons) and an a priori unknown space (the set of all possible stimuli). The intersection patterns are the patterns of firing and silence of those neurons.
Given a cover, it is not difficult to compute the resulting combinatorial intersection patterns. Given just the combinatorial patterns, however, inferring the geometry and embedding dimension of a cover is much harder, and is the central question of my work.
You can find my preprints here.
I enjoy creating 3D sculptures, whether computer-designed and 3D printed, folded and assembled from paper, or just constructed from Legos. I aim to create sculptures that are not only pleasing to the eye, but invite the curious viewer to pick up and play with them.
You can see some photos of my work in the gallery.