# Burkhead, Emily G

Teaching Associate Professor

Phillips Hall 324J

burkhead@unc.edu

## Research Interests

Dynamical systems and ergodic theory, mathematics education

## Professional Background

B.A. College of Wooster, 2001; M.S. University of North Carolina at Chapel Hill, 2004; Ph.D. University of North Carolina at Chapel Hill, 2006; Postdoctoral fellow, Santa Fe Institute, 2006-2007; Assistant Professor / Associate Professor of Mathematics, Meredith College, 2007-2015; Visiting Lecturer and Visiting Researcher, University of North Carolina at Chapel Hill, 2015-2016, 2017 - 2019; Instructor, Duke University; 2016-2017; Cryptologic Mathematician / Applied Research Mathematician / Mathematician, National Security Agency, 2000, 2003, 2004.

## Research Synopsis

My field of study is discrete dynamical systems and ergodic theory, wherein we study the behavior of systems that change over time. The underlying question for a particular system is how predictable or chaotic the behavior is and that can be classified in terms of either topological properties or probabilistic ones. Early work of mine developed a topological classification of a particular type of function called cellular automata that operates on a symbolic space: points in this space consist of an assignment of a state from a finite set to each integer lattice point in n-space. Cellular automata are functions that update each state simultaneously at each time step according to a single rule. Recent work has focused on modeling using stochastic cellular automata, related objects that are not deterministic maps but ones that select from a finite list of rules to apply at each location and at each time step. With Donna Molinek, Davidson College, and Jane Hawkins, UNC CH Emerita, I have analyzed a model for HIV within the lymph nodes, developed and analyzed a model for Ebola within an organ. Currently, my professional focus is on mathematics education and best practices in teaching.

## Representative Publications

*Nondeterministic and Stochastic Cellular Automata and Virus Dynamics*

E.G. Burkhead and J.M. Hawkins,

Journal of Cellular Automata, Vol 13, 103-119, 2018

*A Cellular Automaton Model of Ebola Virus Dynamics*

E.G. Burkhead and J.M. Hawkins,

Physica A: Statistical Mechanics and its Applications, 438, 424-435, 2015

*A Dynamical Study of A Cellular Automata Model of the Spread of HIV in A Lymph Node*

E.G. Burkhead, J.M. Hawkins, and D.O. Molinek,

Bulletin of Mathematical Biology, 71, 25-74, 2009