The notion of strength of a homogeneous polynomial has recently
appeared in the groundbreaking work of Ananyan and Hochster
to resolve Stillman’s conjecture. Since then, it has been extensively investigated.
In this talk, I will first indicate how to determine the strength
of a generic polynomial.
Secondly, using the theory of polynomial functors developed
that bounded strength is not a Zariski-closed condition.
These two results are joint works with Ballico, Bik and Oneto.