Laura's research focuses on singular algebraic geometry, which she describes as the study of "bad" spaces. A sphere, for example, is a "good" space in the sense that it is smooth everywhere and has no corners, knots, or self-intersections. If you were an ant living anywhere on the surface of a sphere (much like we live on the Earth's surface), you would perceive the surface to be relatively flat. Because the sphere is so regular in this way, mathematicians are able to perform calculus-like calculations on the surface of the sphere. On the other hand, a cone-shaped space is "bad" or "singular" at the point of the cone. An ant standing on the point of the cone would not perceive his world to be flat. Calculus can not be done at this "bad" point. Algebraic geometry relates the algebraic and geometric properties of a space and can be used to analyze the properties of such singular points. Her thesis work, "Monomial Generators for the Nash Sheaf of a Complete Resolution", proves that a three-dimensional complex space (that's a six dimensional real space!) with an isolated singular point can be described in strikingly simple terms. She is currently working on an n-dimensional generalization of these results.
When not puzzling over her research, Laura enjoys teaching mathematics. While at Duke University she spent four years developing, teaching, and writing materials for a combined calculus and precalculus course. She is currently writing a textbook that combines calculus, precalculus, and algebra. This textbook is currently in use at JMU, and will be nationally published by Houghton Mifflin in 2004. In her spare time Laura reads way too many science fiction novels, buys too many CDs, stresses too much about politics, obsesses over puzzles, tries to learn to how knit, and plays the piano very badly.
Update: Laura and Phil now have a baby, Calvin Grey Riley! He was born on November 19, 2004. Pictures are at www.filora.com/calvin.html .