In my PhD research, I have developed methods for solving systems of polynomial equations numerically. The focus was on the important class of so-called 0-dimensional systems (i.e. with finitely many solutions). In some approaches such a system is reformulated as an eigenvalue problem, other algorithms solve the problem via numerical homotopy continuation.

I am particularly interested in the important role of toric geometry in the solution of systems of polynomial equations. More specifically, I investigate how homogeneous formulations of the problem in the Cox ring of a certain complete toric variety can help solving (nearly) degenerate systems in a numerically stable way.  

• SIAM AG21, August 2021.