In its board meeting on 10^th May 2021, the Austrian Science Fund FWF has approved Thibaut Verron's grant application "Weighted-homogeneous structure in polynomial equations".

The project concerns the development of algorithms for solving systems of structured polynomial equations. Questions in this context include the design and implementation of algorithms taking into account the structure, as well as the study of their complexity. The proposed work has immediate applications for solving such structured systems, for example in physics.

Furthermore, a better understanding of the weighted-homogeneous structures could lead to algorithmic and complexity improvements regarding polynomial elimination, which is a crucial step in many algorithms manipulating systems of polynomial equations.