Fall 2010, Thursdays, Milner 216, 4:00-4:50 PM

Date: September 30

"  Mini-Talk "
* Prof. Lewis Bowen

* Prof. Jianxin Zhou


L. Bowen: "Entropy in measurable dynamics"

: I have been working to extend results in ergodic theory from actions of amenable groups to non-amenable groups. The most important advance has been in entropy theory. By the 1980s, experts were convinced that there could not be an entropy theory for non-amenable group actions but this has been proven incorrect by my recent work. There are many open problems in this area.

J. Zhou: "Computational Theory and Methods for Solving Nonlinear Multiple Solution Problems"

: The speaker will first present several classes of nonlinear multiple solution problems and explain why people are interested in finding multiple (unstable) solutions. A (focusing/defocusing) Schordinger equation/system will be used as a motivation. Then the speaker will show how two-level optimization/game theory techniques can be used to design numerical methods for finding multiple unstable solutions and how to measure their instabilities and to prove invariance and convergence of the algorithms.
Some interesting numerical results will be presented and several important research directions will be addressed.