Research Information

My primary research interest is in Computer Algebra, although I also have an interest in Computer Science Education and intelligent tutoring systems.

Quantifier Elimination & Computing with Semi-Algebraic Sets
One of the great contributions of Descartes was to connect algebra and geometry. Many of the most common geometric objects - like spheres, cubes, cones, and planes - can be defined with polynomials. Computers can deal with shapes like these by manipulating the polynomials that define them; reasoning about a circle, for example, by reasoning about the equation x^2 + y^2 = 1.

I'm interested in computing with the geometric objects that polynomials define, objects called semi-algebraic sets. This involves a wide variety of topics, from the theory behind algorithms for manipulating such objects to the practical issues of implementing systems that can really perform these computations. Such computations are so demanding that current programs are unable to solve interesting application problems within a reasonable amount of time and space. My ultimate goal is to provide systems for computing with semi-algebraic sets that are powerful enough to be used in scientific and industrial applications.

Much of my research into algorithms ends up implemented in the QEPCAD system for real quantifier elimination and formula simplification by cylindrical algebraic decomposition.