Abstracts for minicourse by James Yorke

November 3 - Chaos and weather prediction

We are using nonlinear dynamics to better determine what the current state of the atmosphere is - so that meteorologists have a better starting point for predictions.  The model of the weather that we use was developed by the National Weather Service.  It has about 3 million variables.

November 10 - Modeling the population dynamics of HIV/AIDS

Our models reveal why the U.S. gay HIV epidemic exploded years before the sub-Saharan epidemic.  HIV entered the U.S. population from African sources.  It thus is surprising that the U.S. gay epidemic exploded over a decade earlier than the African one.  We estimate how the infectiousness of a person varies as the disease progresses.

November 17 - Almost every observation:  a mathematical theory of measurement

When a laboratory experiment (like a moving fluid) is oscillating chaotically, the state of the experiment is revealed only by simultaneously measuring a limited numbers m of variables in the experiment, such as  fluid flow rates at different points, or temperatures or other physical measurements.  In The Republic, Plato has Socrates discuss the very limited nature of observation.  He says we do not see reality but only limited images or shadows of reality.