Fellow 1999-00

Richard S Laugesen


Assistant professor of mathematics

Professor Laugesen came to the University in 1997. He works on mathematical problems inspired by the physical world, but not limited to it. He has studied mathematically how the frequencies of a drum change as mass is redistributed on its surface, and this led to investigations of drums in curved spaces. Recently, he has become interested in nonlinear differential equations, which occur throughout mathematics and science. While two centuries of effort by mathematicians has yielded a thorough understanding of linear differential equations; nonlinear equations regularly mock us with their mysteries. During his Center appointment, he will study the kind of nonlinear differential equations that arise in the modeling of thin fluid films. One regards the solution of such an equation as describing the thickness of a (mathematical idealization of a) fluid film, for each point in space and each time. Since some of these equations have physical origins, one hopes that their solutions will display physical behaviors, like droplet formation (with the solution “beading up” and developing dry spots). Solutions, indeed, sometimes display such behavior in numerical experiments, but there is so far no theoretical explanation for this, and no way of predicting when it will happen. He will work on finding mathematical proofs for such phenomena.