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Burkhead, Emily G

Emily Burkhead

Teaching Associate Professor
Phillips Hall 324J

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