John D. Wiltshire-Gordon
I study the representation theory of categories with applications in algebraic topology. I like configuration spaces, category theory, and computer algebra.
The prototypical situation: a category C acts on a collection of spaces X_c by transformations, and so the induced maps on homology form a C-module. My thesis, completed in 2016 at the University of Michigan under David Speyer, gives theory and algorithms for working with C-modules. I explain how to write a C-module using a presentation matrix and how to use that matrix to compute numbers associated to the module.
Do you have a finitely presented rational FI-module or Fin-module you'd like to understand? Why not try the online calculator, an implementation of my thesis algorithm (source code). You input a presentation matrix over FI or Fin, and the calculator finds its dimension sequence as well its class in K_0. In the case of FI-modules, the algorithm is described here.