Research

My research aims at designing and implementing a well-defined, consistent, and usable category theory language for computer algebra systems.

I am currently working on the CAP project and on the OSCAR project.

Furthermore, I am the developer of the Jupyter kernels for polymake and Singular.

For a more detailed overview of (some of my) projects visit the projects page or see my GitHub page.

CAP project

CAP (Categories, Algorithms, Programming) is a software project for constructive category theory written in GAP. It facilitates both the realization of specific instances of categories and the implementation of generic categorical algorithms. With my colleague Sebastian Posur I gave an introduction at the Université Paris Diderot to constructive category theory and its applications to homological algebra.

OSCAR project

The OSCAR project is meant to be the next generation computer algebra system, combining the power of the four computer algebra systems GAP, Nemo, polymake, and Singular by providing unlimited and full-speed access from and to those systems from julia. It will furthermore provide data structures and algorithms itself that combine functionaliy from all four systems.

Theses

Constructive category theory and applications to algebraic geometry, PhD thesis, Siegen University.

Non-refereed publications

Sebastian Gutche, Deciding kernel membership of the sheafification functor on toric varieties, MFO report no. 25 (2013).