Draisma proved that infinite dimensional varieties of tensors, defined uniformly with respect to the base vector space, are topologically Noetherian up to the action of the general linear group.The infinite power Z^N of a finite dimensional variety Z is ring-theoretically Noetherian up to the action of the infinite symmetric group permuting the copies of Z. We show that infinite powers of infinite dimensional varieties of tensors are defined set-theoretically by the Sym x GL-orbits of finitely many equations. This talk will browse these results.
Joint work with Chiu, Draisma, Eggermont, and Farooq.