Donald G. Saari, Distinguished Professor: Mathematics and Economics, University of California, Irvine, and the 2004 Tom Osborne Visiting Lecturer will deliver the Howard Rowlee Lecture at 4:00 p.m., Thursday, April 8, 2004, 4:00 p.m., Nebraska Union Auditorium. A reception will follow in the Nebraska Union.
Elections: Now that is real chaos!
Abstract: Florida taught us a new four-letter word: chad. But maybe chads are being unfairly maligned. Maybe the real problem is that our election procedures suffer more fundamental problems: problems that "reform" efforts have ignored. Rather than isolated, this general audience expository talk shows, by describing actual elections and results from mathematics, that our standard election procedures are so flawed that we must wonder whether, inadvertently, we decide badly. The problems are much worse and extend: the same "bad decision" effect arises everywhere from academic departments, to corporate board rooms to problems in engineering. Be warned: expect to leave the lecture worried about your last decision.
On Friday, April 9, 2004, Dr. Saari will give two additional talks, one hosted by the Department of Economics and one hosted by the Department of Mathematics.
Arrow's and Sen's theorems; do they REALLY mean what we have been told?
Abstract: Economics and all social sciences involve aggregation and allocation procedures. Serious blows to this area were cast by Arrow's Impossibility Theorem, which essentially states that no decision procedure is fair, and Sen's Theorem, which claims there is a fundamental conflict between individual liberties and the kind of welfarism commonly assumed to hold in economics. (Both seminal results played central roles in Arrow's and Sen's Nobel awards.) But, do these fundamental assertions really mean what we have commonly assumed they do for the last 50 and 30 years? After introducing these assertions, I show that they do not mean what we have thought. Of particular importance, by identifying why these results arise, resolutions are forthcoming—and we learn how the same problem plagues other economic constructs.
The evolution of Newton's Universe
Abstract: After Newton developed his equations of motion, he found the solution for the two body problem. Reportedly, the three-body problem—a sparse system consisting of only three particles such as the Sun-Earth-Moon—gave him a headache: it has been giving mathematicians and astronomers headaches ever since. But, over the last couple of decades, significant progress has been made. In this expository talk, the "chaotic" reasons for Newton's headache are described, the impact the N-body problem has had on mathematics is suggested, and an outline of what we know about the evolution of Newton's universe (for any number of particles) is provided.
Note: This math talk will be expository and, while new results will be given, it should be understandable to graduate students and even some bright seniors.