Strength of (infinite) polynomials

Talk - Mathematics
The topic of this talk is the strength of polynomials (previously known as Schmidt rank)
defined by Ananyan and Hochster in their paper proving Stillman's conjecture. It is the
minimal number of reducibles that sum up to the polynomial. In many settings, one can
divide polynomials into two classes, those of high strength and those of low strength, and
investigate these classes separately. By definition, polynomials of low strength have
structure in the sense that they have a description in terms of a small number of lower
degree polynomials. For high strength polynomials, we search for other kinds of structure.
During the talk, I will discuss ways in which polynomials of high strength are similar to
(infinite) polynomials of infinite strength, which are often easier to understand.