This award will support an NSF/CMBS regional conference to be held at West Chester University of Pennsylvania in the summer of 2012 on the topic of mathematics applied to social and behavioral problems. The principal speaker will be Professor Donald Saari from the University of California at Irvine. This award will support 30 participants at different stages of their careers.
After an introductory lecture, Professor Saari's presentations will focus on the following topics: symmetries and paired comparisons, impossibility theorems, symmetries and voting problems, applications of symmetries to more general decision problems, dynamics of social and behavioral systems, and topological structures applied to psychology. He will conclude with a presentation on open problems.
. Donald Saari of the University of California, Irvine was the principal speaker. At UC Irvine, Saari is a professor of mathematics and economics and he directs the Institute for Mathematical Behavioral Sciences. Professor Saari gave two 90-minutes lectures daily during the week of August 13. He described how he has used algebraic topology, simplicial geometry, chaos theory, and differerential geometry to solve problems in voting theory, economics, and psychology. The two main goals of this conference were to make mathematicians, young and old, aware of the open problems in the social and behavioral sciences and to present some of the tools that have been used to solve other similar problems. It is hoped, as a result of this experience, that conference participants will collaborate with social and behavioral scientists in the future. Most of the participants described themselves as dabblers in many areas. This trait is a good one to have in this area – the more mathematics one knows, the more problems one can solve. As the week came to a close, several participants told me that this was one of the best conferences they had ever attended. As usual, Saari did a top-notch job; he is very charismatic and knowledgeable. Including Saari and myself, there were 40 participants. There were 29 participants supported by the conference grant; 30 men and 10 women; 11 students and 29 faculty; and 6 people of Asian descent, 4 of Indian descent, 6 of African descent, and 2 of Arabic descent. In the coming year, Donald Saari will produce a monograph based on his lectures this past summer. It will be published by the Society for Industrial and Applied Mathematics (SIAM).
