Software

For all my code, please visit my GitHub page (see https://github.com/pgallardo)

1. Variations of GIT quotients package (2016)

In joint work with Jesus Martinez-Garcia (University of Essex, UK), we developed software, in Python, that calculates the computational information required to describe the GIT quotients parametrizing a pair defined by hypersurface and a hyperplane. The mathematical background is found in our article "Variations of geometric invariant quotients for pairs, a computational approach" and an application is described in our article "Moduli of cubic surfaces and their anticanonical divisors." A detailed description of the program's output and license can be found here. For the articles, please look at my homepage.

2. Quivers and their thin sincere representations

In work with Mary Barker (WashU), we study thin-sincere representations of acyclic quivers, i.e., dimension vector equal to (1, ..., 1). In particular, we develop a Macaulay2 package to completely describe their geometry and moduli spaces.