Pitzer College

Abstract: I'll recount seven myths about the development of mathematics that I have encountered in my career as a historian of mathematics. For instance, here's one you have probably encountered too: It is often said that Newton invented the calculus just to do his physics. Did he?

The examples to be discussed range from antiquity to the twentieth century. I hope to provide a more accurate (and more interesting!) story for each. I will also also explain what is at stake in getting each of them right: the general point is that it helps us understand the way mathematics actually develops and thus helps us--and the rest of humanity--realize what a neat subject we have.

California Institute of Technology

Abstract: In this work the generalized vortex method of Baker, Meiron, and Orszag (1982) is applied to study the evolution of the instability observed when a shock wave goes through a perturbed interface separating two different gases (the classical single-mode Richtmyer-Meshkov instability) and the instability generated by a shock passing through an oblique interface (the Richtmyer-Meshkov instability at oblique interfaces). The initial vorticity deposited by the shock on the interface is modeled exactly using the asymptotic formulae of Zabusky and Samtaney (1994). The mixing layer width, bubble and spike velocities computed from the vortex method are compared with analytic models and wiht results from high-resolution Weighted Essentially Non-Oscillatory (WENO) simulations.

UC San Diego

Abstract: A classical problem in geometry deals with finding the densest packings of equal discs in the Euclidean plane. While the solution to this problem has been known for more than a hundred years (hexagonal is best), there are many variations of this problem which are completely unsolved. In this talk, I will describe some of what is currently known, and what is still unknown.

1:30, Beckman Auditorium, HMC

(Tea at 1:00)

UC Irvine

Abstract: As battery-operated embedded systems proliferate, energy efficiency is becoming an increasingly critical consideration in system design. This talk will survey algorithmic problems that arise in minimizing power consumption at the operating systems level. In particular, we will examine two different mechanisms to reduce energy consumption: 1) if a system or device is idle it can be put into a low-power sleep state, 2) running tasks more slowly can result in reduced energy consumption. We will discuss several different optimization problems that arise in using these power-reducing mechanisms. We will discuss some solutions to the first of these problems: devising effective power-down strategies.

Harvey Mudd College

Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using various tools. In this talk, we demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. You will enjoy the magic of Fibonacci numbers, Lucas numbers, continued fractions, and more. You can count on it!

This talk is based on research with Professor Jennifer Quinn and many, many undergraduates.

Harvey Mudd College

Abstract: When mathematical objects have a social interpretation, the associated theorems have social applications. We give a few examples, including joint work with A. Niedermaier (HMC '04) on a set-covering theorem for trees and cycles, with connections to topology and combinatorics, and joint work with D. Berg (HMC '06) with an application to voting.