Much of Burns' research has centered on mathematical issues that arise when developing computational methods for control, design and optimization of infinite dimensional systems. He has worked on a variety of problems including the theory of functional differential equations, computational control theory, structural control, control of fluid flows, smart materials, nano-technology, aerodynamics, mathematical biology, energy efficient buildings and sensitivity analysis. Burns has worked on many aspects of applied mathematics, ranging from highly theoretical analysis to the development of numerical algorithms and computational tools that can be used to address a broad range of practical engineering and scientific problems.
Burns received his M.S.E. in mathematics in 1968 from Arkansas State University and his Ph.D. in Mathematics from the University of Oklahoma in 1973 under the direction of Professor Reid and he joined Brown University as a postdoctoral fellow in the Lefschetz Center for Dynamical Systems. He has been a professor of mathematics at Virginia Tech since 1974. Burns has been a consultant and advisor to Booz Allen & Hamilton, NASA Langley Research Center, the Air Force Research Laboratories, DARPA, The Babcock and Wilcox Company, Solers Inc. and United Technologies. He has held several academic visiting positions in the USA, Europe and Asia. He has served on more than 12 editorial boards and he was the founding Editor of the SIAM Book Series on Advances in Design and Control. He has served as Vice President of SIAM, as Chair of the SIAM Activity Group on Systems and Control and has been a Fellow
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