Hotelling Lectures by Professor Thomas Kurtz

Lecture 1, Monday April 7, 2008
4:00-5:00pm, Manning Hall 209 (Reception 5:00-6:00pm, Howell Hall)
Title: Stochastic models for chemical reactions

Abstract:  Attempts to model chemical reactions within biological cells have led to renewed interest in stochastic models for these systems. The classical stochastic models for chemical reaction networks will be reviewed, and multiscale methods for model reduction will be described.  The methods will be illustrated with derivation of the Michaelis-Menten model for enzyme reactions and a simple model of viral infection of a cell.
Lecture note
  

Lecture 2, Wednesday April 9, 2008
4:00-5:00pm, Smith Hall 107 (Reception 3:30pm-4:00pm, Smith Hall 202)
Title: Identifying separated time scales in stochastic models of reaction networks

Abstract:  Reaction rates and chemical species numbers may vary over several orders of magnitude.  Combined, these large variations can lead to subnetworks operating on very different time scales.  Separation of time scales has been exploited in many contexts as a basis for reducing the complexity of dynamic models, but the interaction of the rate constants and the species numbers makes identifying the appropriate time scales tricky at best.  Some systematic approaches to this identification will be discussed and illustrated by application to a model of the heat shock response in E. Coli. 

Lecture 3, Friday April 11, 2008
4:00-5:00pm, Smith Hall 107 (Reception 3:30pm-4:00pm, Smith Hall 202)
Title: Averaging fast subsystems

Abstract:  Reducing the complexity of system models by averaging fast subsystems has a long history in applied mathematics in general and for stochastic models in particular.  The previous lectures exploited ad hoc, stochastic analytic relationships to derive the desired averages.  This lecture will focus on more systematic methods based on the martingale properties of the underlying Markov processes.