Noetherianity up to symmetry

In this talk, we will follow the paper “Noetherianity up to Symmetry” (Combinatorial Algebraic Geometry Volume 2108 of the series Lecture Notes in Mathematics, pp. 33-61) by Jan Draisma. We will discuss Noetherianity up to the action of a monoid in the setting of infinite-dimensional algebraic geometry. Many of the classical algebraic varieties come naturally in families. The equations of all varieties in these families have remarkably the same structure. The notion of equivariant Noetherianity encodes and explains such a behaviour. We will discuss some examples and applications from the cited paper.