My research area "Computational Tropical Algebraic Geometry" is concerned with the interplay between polynomial equations, polyhedra and algorithms. Ideally algortihms are implemented and applied. In the same way that we know that a general quadratic polynoial has (at most) two solutions because its degree is two, polyhedra can be used to argue about multivariate systems of polynomial equations. A long term goal is to push these methods as far as possible on Smale's 6th problem in celestial mechanics.
I have been lecturing the bachelor course "Algebra" since 2019. When possible I emphasise the last chapter of the text book about Gröbner bases. This theory is background material for a good part of the bachelor projects that I supervise. Other topis for bachelor and master theses are related to "Graph Theory 2" that I was teaching in the Math-Economy porgramme. Typically projects are concerned with algorithmic or combinatorial aspects of math. Other topics for my master courses have been in tropical geometry and polynomial system solving.
