Carter completed his PhD in applied mathematics at UC Davis in 2020. His research was on developing and analyzing differential equations models of neurolocomotion in the nematode C. elegans in order to understand the biophysical mechanisms of its coordination. Carter moved to the University of Utah as a Wylie Research Assistant Professor to develop mathematical models of astrocyte-neuron interactions, specifically examining how astrocyte-mediated changes in synaptic ion concentrations affect neuronal signalling. He has also taught a number of mathematical biology-focused courses, including calculus, statistics, and modeling with differential equations.
