Cecilia Diniz Behn

Professor, Applied Mathematics and Statistics
Joe & Jane Gray Distinguished University Chair

I am a Professor in the Department of Applied Mathematics and Statistics at Colorado School of Mines. I also have an appointment as an Adjoint Associate Professor in the Department of Pediatrics at the University of Colorado School of Medicine.

Education

• PhD, Mathematics. Boston University, Boston, MA (2006)
• MA, Mathematics, University of Texas, Austin, TX (2002)
• AB, Mathematics, magna cum laude, Bryn Mawr College, Bryn Mawr, PA (1999)
• Budapest Semesters in Mathematics, Technical University of Budapest, Budapest, Hungary (Spring 1998)

Research Areas

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. I also develop novel, neurscience-inspired approaches for investigating artificial neural networks in support of machine learning interpretability.

During the course of my graduate training in the Department of Mathematics and the Center for BioDynamics at Boston University; my postdoctoral training in the Division of Sleep Medicine at Harvard Medical School and the Department of Mathematics at the University of Michigan; and my faculty appointments, I have developed a strong, externally-funded research program in applied math with vital connections to biomedical research.

Current Research Projects

• Multiple time scales in the interactions between sleep and circadian rhythms
• Regulation of rapid eye movement (REM) sleep
• Orexin/hypocretin neurons and their role in stabilizing sleep-wake behavior
• Glucose-insulin dynamics and quantifying tissue-specific insulin resistance
• Inferring insulin secretion rate and quantifying beta cell function
• Neuroscience-inspired machine learning interpretability

Recent Courses

• MATH 331/431 Mathematical biology
• MATH 472/572 Mathematical and computational neuroscience
• MATH 501 Applied analysis (measure theory & functional analysis)
• MATH 510 Differential equations and dynamical systems