Algebraic topology solves geometric and topological questions by using algebraic information that can be distilled out of the spaces involved. The algebraic structures that arise in this way are quite interesting in their own right. My work has investigated them both for their intrinsic interest and for their usefulness in solving topological problems.
One of the key tools that I have used a lot is called the Adam spectral sequence. Some applications of it require as input an algebraic calculation about which we have only partial information. I have written computer code that is quite efficient at producing big (but finite) pieces of these calculations. This code is used by a number of other algebraic topologists around the world.
My masters student, Michael Catanzaro, has also written a package of sage code to work with finitely presented modules over the Steenrod algebra.
The projects I am proposing here would involve working with one of these two software packages to enhance and extend their capabilities and usefulness.