Jonathan Mattingly is associate professor of mathematics and statistics at Duke University. He works primarily in stochastic dynamics, stochastic modeling, and stochastic analysis. He is interested in both specific models and more general questions of pure stochastic analysis motivated by applied questions. The central mathematical issue is how to discover, characterize, and prove the qualitative behavior of classes of stochastic dynamical systems. In the biological context, he has worked on a number of problems related to stochastic fluctuations in biochemical networks. He is currently studying large chemical networks using ideas from averaging to obtain effective reduced dynamics. He is also interested in the qualitative behavior of specific small dimensional networks of biological importance. He works on numerical issues in simulating stochastic differential equations, both long time simulations, higher order methods, and adaptive methods. Recently, he has also started working on modeling flu evolution and transition.
We will lecture on the long time behavior of Markov processes starting from simple Markov chain examples and moving to more complicated examples. He will give an introduction to basic ergodic theory and discuss topics such as meta-stability, quasi-invariant measures, and the rate of convergence to equilibrium. Examples will be drawn from physical and biological systems.