My research interests lie in the field of commutative algebra, specifically tight closure theory, characteristic p methods, and big Cohen-Macaulay algebras and modules.
I study generalized number systems (called “rings”) that behave like the integers or real numbers in many ways but can also behave quite differently. Such systems arise when one studies solutions to systems of equations. I am particularly interested in rings where a fixed number (usually prime) is set equal to 0. (Imagine how 24 = 0 in a 24-hour clock.) Rings also possess geometric information, just as the solutions to y=x^2 can be thought of as a parabola in the plane. Moving back and forth between the algebra and geometry involved can often help one understand both areas better.
I have also written on the history of how algebra (specifically, the negative exponent) has been taught in high school in the United States and worked with some colleagues in Biology on issues related to statistical analysis of qPCR data.