## Professor David E. Keyes

Department of Applied Physics and Applied Mathematics

Columbia University

S. W. Mudd Building 215, MC 4701

500 W. 120th St.

New York, NY 10027

E-mail: david.keyes@columbia.edu

Professor Keyes has degrees in engineering (B.S.E., 1978, Princeton) and applied mathematics (Ph.D., 1984, Harvard) and held post-doctoral and faculty positions at Yale before moving into computer science at Old Dominion in 1993 and into the parallel numerical algorithms research group at NASA Langley's Institute for Computer Applications in Science and Engineering (ICASE). In 1999, he became the Acting Director of Lawrence Livermore National Laboratory's Institute for Scientific Computing Research, a program fostering academic collaborations at the laboratory, especially in support of the ASCI program. In 2001, he was named the first Director of Old Dominion's Center for Computational Sciences and became lead investigator on a nine-institution Integrated Software Infrastructure Center for Terascale Optimal PDE Simulations (TOPS), as part of the Department of Energy SciDAC Initiative. He works on architecture-sensitive multi-level domain-decomposition algorithms for partial differential equations, with special interest in applications to fluid dynamics, radiation transport, and magnetohydrodynamics.

**What's Math got to do with it?**

Mathematics has acquired a number of stereotypes that may discourage even the most capable students from the major and prevent people in general from recognizing its permeation into almost everything else they value in life. In this talk, we face some of these stereotypes and consider whether they are justified. In so doing, we point out dozens of applications from pace-setting science to contemporary entertainment, from chart-topping business to national security, from leading-edge medicine to consumer products, where a good share of the excitement in the field is actually in the mathematics. We briefly learn to "read" a differential equation and consider how to map its solution onto a computer. Our goal is to show that mathematics is a vibrant field, worthy of study at the college level by majors and nonmajors alike. In fact, just as the English language is spoken by more people who are not native speakers than by natives, mathematics is used daily by more people who are not professional mathematicians than by professionals.

**How Many Computers Fit on the Head of a Pin?**

This elementary lecture introduces the idea of real-time computational simulation of fluid flow around an aircraft. It leads, through some initial naive assumptions, to the conclusion that this problem is not computable with any technology, due to nonnegotiable physical constants like the speed of sound in the atmosphere and the speed of electronic signals (close to the speed of light) in semiconductors. As the naive assumptions are replaced with more practical compromises, involving computer architecture and mathematical modeling, a computable problem comes into view. The presentation touches upon the discretization of a continuous mathematical problem and the distribution of a computation over the processors of a large-scale parallel computer. To illustrate, some videotaped comparisons are shown between computations and windtunnel experiments of vortical flows over delta-wing aircraft.

The presentation requires an overhead slide projector and a VHS VCR system to play the videos.

**Scientific Discovery through Advanced Computing**

The Scientific Discovery through Advanced Computing (SciDAC) initiative is a web of interconnected projects—partly research and partly software development --- designed to support simulation, data exploration, and collaboration in many thrust areas of the U.S. Department of Energy, including: climate modeling, fusion energy, chemical and materials science, astrophysics, and high energy and particle physics. SciDAC supports the creation of a new generation of scientific simulation codes for terascale systems. The program also includes research on numerical algorithms and systems software that will allow these codes to use modern parallel computers effectively. SciDAC will be of interest to modelers and researchers for the freely available software it will produce, and its approach is already being imitated in Europe and Asia. The acclaimed solver software "PETSc" is part of the nine-institution "Terascale Optimal PDE Simulations" (TOPS) project within SciDAC. As the director of the TOPS project, the speaker will provide an overview of its scope and scientific goals at a "big picture" level.