## Geometry Seminar

**Date: ** March 20, 2023

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 628

**Speaker: **Arthur Bik, IAS and MPI Leipzig

**Title: ***Strength of infinite polynomials*

**Abstract: **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.