The Stanford University Mathematical Organization recently began a speaker series. The goal of the series is to let students listen to professors discuss their backgrounds and research, as well as to let students hear some interesting problems or ideas.
May 25, 1999: Professor Robert Finn, "Capillary Surface Interfaces", 5:30 PM, Room 380-380C
The mathematical ideas underlying capillarity theory were introduced almost two centuries ago by Thomas Young, who professed to despise mathematics. Formal equations were derived by Laplace, and a unifying conceptual basis was provided by Gauss. The elegant formal simplicity of the equations is deceptive, and until recently there was no general theory on existence or behavior of solutions. For the three dimensional case with uniform gravity field, not a single explicit solution has yet been discovered. The first general existence theorem did not appear until 1973, and in fact existence can fail in some unanticipated ways. Seeming experimental anomalies have led to questioning of the physical adequacy of the equations.
This talk will describe new studies (in some of which Stanford students participated) that show discontinuous dependence of solutions on the boundary data, symmetry breaking, failure of existence under physical conditions, and failure of uniqueness under conditions for which solutions exist. Some of the predictions have been verified in space experiments, and the experimental confirmations offer convincing evidence in support of the physical correctness of the equations as originally formulated. The predictions are suggestive for applications, notably for fluid management under low gravity conditions.
Professor Finn has been a member of the Stanford faculty since 1959. In addition to permanent positions, he has held numerous visiting professorships in Germany, Italy and Taiwan. Apart from academia, he was a consultant to the European Space Agency for the design of space experiments in 1987 and has been an investigator for NASA space shuttle experiments since 1990. He was twice awarded the Guggenheim award, once in 1958 and another time in 1965.
"Which integers are the areas of right triangles with three rational sides? This question was written down in Arab manuscripts more than 1000 years ago and the answer turns out to be related to the existence of rational points on certain elliptic curves. Elliptic curves are curves defined by equations y^2 = f(x) where f(x) is a cubic polynomial, and they are a powerful tool for attacking many old and new number theoretic problems. They have also found applications in cryptography. This lecture will They have also found applications in cryptography. This lecture will introduce elliptic curves and discuss some deep open questions in this field."
Professor Rubin came to Stanford in 1997 and has spent most of his research career studying elliptic curves. He graduated with a AB from Princeton in 1976 (where he was a Putnam Fellow) and went on to Harvard to get a Ph. D in mathematics in 1981. He was the first Ph.D. student of Andrew Wiles, who used elliptic curves to prove Fermat's Last Theorem. He has won various awards for his work, including the AMS Cole prize in number theory in 1992 and a Guggenheim Fellowship in 1994.
April 8, 1999: Professor Persi Diaconis, "Mathematics and Magic"
"Sometimes the way a magic trick works is just as amazing as the trick itself. I will demonstrate with examples. These mathematics have applications beyond magic, ranging from, among others, rhyming patterns in Indian music, cryptography and robot vision."
Persi Diaconis has led a double career in magic and mathematics. He left home at age fourteen and made his living as a magician until age twenty-four, having started out as assistant to the greatest sleight-of-hand worker of the era, Dai Vernon. Following extensive training in the applied probability of card shuffling, he went back to college to learn the theory behind it, and continued with a Ph.D. in mathematical statistics at Harvard University. He was awarded a MacArthur Fellowship in 1982, and held positions in statistics at Stanford and in mathematics at Harvard. He has just returned to Stanford University, where he has been named the first Mary V. Sunseri Professor in the School of Humanities and Sciences, with a joint appointment in Mathematics and Statistics.