241001 Josefien Kuijper

In algebraic geometry, we study algebraic varieties: geometric objects that can be described by polynomials. They can be inspected using instruments which I call invariants. An invariant assigns to each variety an object (this can be a number or a group element, but also a group or a vector space, or even a category) that is invariant under isomorphisms of varieties. A “good” invariant moreover remembers some of the relationships that are present between different varieties; more formally, one can say that such an invariant satisfies a “descent property”. In this talk, I will discuss how descent properties can help us understand invariants of varieties better, and potentially construct new ones.