I am an assistant professor in the Department of Applied Mathematics and Statistics at Colorado School of Mines. I also have an appointment as an adjoint assistant professor in the Department of Pediatrics at the University of Colorado School of Medicine.
My research applies multiscale mathematical modeling to investigate key research questions in metabolism, sleep, and circadian rhythms. Specifically, I model key dynamics in whole-body metabolism including changes in glucose, glycerol, and insulin; sleep and circadian (~24 h) neurophysiology; and the diverse interactions among these systems. Dysregulation of metabolism and/or sleep has dramatic implications for human health, and the complex ways in which these systems interact, both on a mechanistic and on a behavioral level, are just beginning to be understood. My research in mathematical and computational neuroscience focuses on understanding neurophysiologic mechanisms for sleep/wake regulation and my work in whole-body glucose-insulin dynamics focuses on insulin resistance in adolescents.
Mathematically, my research contributes to the development of novel techniques to understand high-dimensional multiscale systems of differential equations; analyze connections between structure and dynamics of general networks; and investigate dynamics at the interface of deterministic and stochastic behavior.
During the course of my graduate training in the Department of Mathematics and the Center for BioDynamics at Boston University and my postdoctoral training in the Division of Sleep Medicine at Harvard Medical School and the Department of Mathematics at the University of Michigan, I have developed a strong, externally-funded research program in applied math with vital connections to experimentalists and clinicians.
Current research projects address the following:
- Multiple time scales in the interactions between sleep and circadian rhythms
- Glucose-insulin dynamics tissue-specific insulin resistance
- Orexin/hypocretin neurons and their role in stabilizing sleep-wake behavior
- Stochastic and deterministic contributions to the fine architecture of sleep-wake behavior
My research is or has been supported by the following extramural grants:
- National Science Foundation Grant DMS 1412571 (2014-2017)
- National Science Foundation Grant DMS 1121361 (2011-2014)
- Air Force Office of Scientific Research Grant FA9550-08-1-0111 (2008-2011)
Current teaching - Spring 2016
MATH 498/598 Mathematical and Computational Neuroscience