I am interested in the theory and applications of dynamical systems. My theory interests include counting and characterizing fixed points of area-preserving dynamics, studying properties of chaotic dynamics, and trying to understand the basics of real algebraic geometry.
My applied interests focus on challenging the mathematical underpinnings of neo-classical general equilibrium theory in economics, and on building and analyzing transmission models of communicable diseases, such as HIV, staph infection, and malaria. I use these disease models to estimate parameters, such as contagiousness and contact structures, and to compute thresholds for disease take-off, especially using a Liapunov function approach.
I was the founding director of the UM Center for the Study of Complex Systems, and am the director of the U-M Science and Technology Public Policy Program.
