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.
April 19, 2000: Professor Rafe Mazzeo, "Spectral Geometry and Scattering Theory"
"This talk will be about some of the basic problems of spectral geometry. This subject attempts to find connections between the geometry of a domain in the plane (or some more complicated surface or manifold) and what is known as the `spectrum' of the Laplacian on that domain or surface. Basic questions include the famous one of whether it is possible to detect the shape of a musical instrument if one knows all of the overtones it can produce. If there is time at the end, I will also discuss some closely related questions in quantum theory.
It will be useful, but not required, to have some knowledge of ODE's and linear algebra, for this talk. (This talk is intended for undergraduate or graduate students and anyone else who is interested in mathematics!)"
February 23, 2000: Professor Yakov Eliashberg, "Inverting a 2-Sphere Inside Out"
"We will discuss Smale's theorem which has a counter-intuitive corollary stated in the title, and its far-going generalizations."
January 20, 2000: Ted Hwa, "Combinatorial Game Theory", 5:30 PM, Room 380-380C
"Games have fascinated mankind since the earliest times, yet it is only recently that a general mathematical theory, applicable to a wide variety of games, has emerged. Known as Combinatorial Game Theory, the theory studies two-player chanceless games in which the object of the game is to move last. It has been applied to games as different as nim, chess, and go. In this talk, I will introduce the theory, beginning with the game of nim. We will see that every finite, impartial combinatorial game essentially reduces to nim. Impartial means that the players do not 'own' the instruments of play, so that both sides choose from the same set of legal moves. If time permits, I will discuss the general case, as well as applications of the theory to actual games."
Ted did his undergraduate work in computer science at Stanford. He is a second year graduate student in mathematics. His main research interest is number theory. However, games (board games, card games, etc.) have always been somewhat of an obsession, so he has studied some combinatorial game theory to understand how mathematics can be applied to games.
November 11, 1999: Professor W. Hugh Woodin (University of California at Berkeley), "Solving Unsolvable Problems", noon, Room 380-383N
One approach, which has been quite successful, to dealing with unsolvable problems is the introduction of (new) axioms of infinity. Prof. Woodin will discuss and give examples of fairly "concrete" mathematical problems which are formally unsolvable but nevertheless "solvable" through the introduction of axioms of infinity in various forms.
October 25, 1999: Professor Brian White
"Dip a bent loop of wire into soapy water, pull it out, and you will see a beautiful soap film. Efforts to understand such soap films have led to very many important discoveries in mathematics. This lecture will present a few examples."
Professor White graduated from Princeton University with a Ph.D. in mathematics in 1982 and has been at Stanford since 1983. Apart from his positions in Stanford, he has held visiting positions in numerous overseas institutions. His primary research interests are geometric measure theory, differential geometry and minimal surfaces. His awards include a Sloan Fellowship, Presidential Young Investigator, Bing Teaching award and most recently, a Guggenheim Fellowship this year.