Polynomial functors as affine spaces

Abstract: Polynomial functors are like spaces of objects (e.g. k-way tensors) without fixed size and come with an action of (products of) general linear groups. The aim of this talk is to answer the following question: what happens when you replace vector spaces by polynomial functors when defining affine spaces?

I will define polynomial functors, the maps between them and their Zariski-closed subsets and give examples of these things. Then, I will discuss how to extend some of the basic results from affine algebraic geometry to this setting. This is joint work with Jan Draisma, Rob Eggermont and Andrew Snowden.

commutative algebraalgebraic geometry

Audience: researchers in the topic

Max Planck Institute nonlinear algebra seminar online

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