Message from the Chair

For over two thousand years mathematics has been characterized by rigor and infallible reasoning through theorem-proof. This characteristic and its utility in problem-solving have placed the subject at the core of science and engineering.

One indication of the significance of ongoing mathematics research is the multitude of applications that are in development. In the case of our department, faculty are engaged in research that is being applied in computer network security, image recognition, digital representations of three-dimensional objects, and the management of financial portfolios, to name a few examples. Gunther Uhlmann, the inaugural Walker Family Endowed Professor, describes in an article the applications of his research to medical imaging. Another faculty member working in the same research area, John Sylvester, is engaged in a collaboration that focuses on the detection of land mines. In addition to applying existing theory, such projects yield experimental data that will feed into new theorems. Theory motivated by applications will often identify critical properties, or make predictions, which can then guide the experimentalist. Collaboration and interaction are the crucial words.

Mathematicians develop mathematical structures and ideas, and aim to understand relationships between different parts of the mathematical fabric. This quest is guided by a desire for absolute truth and a notion of beauty that is very real to the trained mathematician. It relies on insight researchers sharpen through experience, and is often motivated by fundamental examples. Computers have made it possible to call upon examples that were previously beyond reach. William Stein, who joined our department this year, complements his work in number theory with a project called SAGE: Software for Algebra and Geometry Experimentation, whose purpose is to create a unified open source mathematics package. The students who work on this project are introduced to mathematical ideas and research in an environment that is rare in mathematics, though not dissimilar to that of a scientific lab. An article by Sándor Kovács, the inaugural McKibben and Merner Endowed Professor, describes his research at the crossroads of two of the main branches of mathematics, where polynomials and geometric objects meet.

Vigorous research is fundamental to everything the Department does. It brings excellent faculty members to the Department, who hold the key to our continuing success in research and education – missions that are inextricably linked. We have had the privilege of attracting excellent graduate students and some of the strongest UW undergraduate students into our programs. You will read in the following pages about some of their achievements. It is a pleasure to offer students an environment of research and education in which they can thrive as they acquire the mathematical training that carries them into the future. We are grateful to the Department's alumni and friends for their support of our work.

Selim Tuncel