| Kathleen A. Hoffman
I have been with the Mathematics and Statistics department at UMBC since 1999. Before joining UMBC, I was a postdoctoral member of the Institute for Mathematics and its Applications (IMA) from 1997-1999 during the theme years of Emerging Applications of Dynamical Systems and Mathematical Biology. I received my Ph.D. in applied mathematics from the University of Maryland at College Park in 1997, under the direction of John H. Maddocks.
My research interests include stability theory for constrained calculus of variations problems bifurcation theory for multiple timescale systems, neuromechanical locomotion, epidemiology, ecology, and phototransduction. My dissertation research focused on the development of two particular tests for stability of solutions to variational problems: distinguished diagram theory and conjugate point theory. I used these tests to determine the stability of an elastic loop, a well-known model for DNA minicircles. Since then, along with my collaborators, John Maddocks, Rob Manning , Randy Paffenroth , and Fadil Santosa , I have used permutations of this theory to understand the stability of three-dimensional elastic struts, welding and clamping of sheet metal, and multiple-covered circles with inherent curvature.
My interest in multiple timescale systems developed during my postdoctoral years at the IMA. Along with my collaborators, John Guckenheimer, Warren Weckesser, I developed a theory of global bifurcations of systems with two time scales, using the forced van der Pol equation as a model system. These bifurcations are intricately connected to the canard solutions of the system.
I spent my sabbatical (2006-2007) working in Avis Cohen's Neurolocomotion Lab in College Park MD. Building on that experience, I developed a research program in sensory feedback in neuromechanical locomotion in collaboration with Avis Cohen, Tim Kiemel, Eric Tytell, Phil Holmes , Lex Smits, Lisa Fauci , and Thelma Williams. We are concerned with developing, understanding and analyzing components of lamprey swimming: from nerve conduction along an axon, to muscle contraction and body dynamics to interaction with the fluid environment. Our group recently received a grant from NSF RCN-PLS Neuromechanics that will facilitate collaboration activities that include exchange visits of graduate students and postdoctoral fellows among RCN laboratories, an annual Winter Workshop on Locomotion, and visits among members of the RCN network.
I am actively involved in three UMBC grants focused on the interface between mathematics and biology:
I am a member of the