The geometry of polynomial functors

Abstract: A polynomial functor P is a functor from the category of finite-dimensional vector spaces to itself such that for every U,V the map Hom(U,V) -> Hom(P(U),P(V)) is polynomial. In characteristic zero, P is a direct sum of Schur functors.

This talk concerns closed subsets of such P, i.e., rules that assign to a vector space V a closed subset X(V) of P(V) such that P(phi)X(U) is contained in X(V) for every linear map phi:U -> V.

Quite surprisingly, these behave very much like finite-dimensional affine varieties. For instance, they satisfy the descending chain condition and a version of Chevalley's theorem on constructible sets. I will discuss these results and more. The talk is based on joint work with Arthur Bik, Rob Eggermont, and Andrew Snowden.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologymetric geometryquantum algebrarepresentation theory

Audience: researchers in the topic

Sapienza A&G Seminar

Series comments: Weekly research seminar in algebra and geometry.

"Sapienza" Università di Roma, Department of Mathematics "Guido Castelnuovo".