21 citations · 106 across the 19 of their papers we have counts for
19 papers
Improved unirationality for GL-varieties
Arthur Bik, Jan Draisma, Rob Eggermont +1
A -variety is a typically infinite dimensional variety equipped with a suitable action of the infinite general linear group . In earlier work, we establis…
Global Positioning on Earth
Mireille Boutin, Rob Eggermont, Gregor Kemper
Contrary to popular belief, the global positioning problem on earth may have more than one solutions even if the user position is restricted to a sphere. With 3 satellites, we show…
Topological Noetherianity of the infinite half-spin representations
Christopher Chiu, Jan Draisma, Rob Eggermont +2
We prove that the infinite half-spin representations are topologically Noetherian with respect to the infinite spin group. As a consequence we obtain that half-spin varieties, whic…
Uniformity for limits of tensors
Arthur Bik, Jan Draisma, Rob Eggermont +1
There are many notions of rank in multilinear algebra: tensor rank, partition rank, slice rank, and strength (or Schmidt rank) are a few examples. Typically the rank locus…
Image closure of symmetric wide-matrix varieties
Jan Draisma, Rob H. Eggermont, Azhar Farooq +1
Let be an affine scheme of -matrices and be an affine scheme of -dimensional tensors. The group Sym$(\mathb…
Sym-Noetherianity for powers of GL-varieties
Christopher H. Chiu, Alessandro Danelon, Jan Draisma +2
Much recent literature concerns finiteness properties of infinite-dimensional algebraic varieties equipped with an action of the infinite symmetric group, or of the infinite genera…
Quasihomomorphisms from the integers into Hamming metrics
Jan Draisma, Rob H. Eggermont, Tim Seynnaeve +2
A function is a -quasihomomorphism if the Hamming distance between and is at most for all . We show…
Universality of high-strength tensors
Arthur Bik, Alessandro Danelon, Jan Draisma +1
A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given p…
The geometry of polynomial representations
Arthur Bik, Jan Draisma, Rob H. Eggermont +1
We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms…
Components of symmetric wide-matrix varieties
Jan Draisma, Rob H. Eggermont, Azhar Farooq
We show that if X_n is a variety of cxn-matrices that is stable under the group Sym([n]) of column permutations and if forgetting the last column maps X_n into X_{n-1}, then the nu…
Polynomials and tensors of bounded strength
Arthur Bik, Jan Draisma, Rob H. Eggermont
Notions of rank abound in the literature on tensor decomposition. We prove that strength, recently introduced for homogeneous polynomials by Ananyan-Hochster in their proof of Stil…
Topological noetherianity for algebraic representations of infinite rank classical groups
Rob H. Eggermont, Andrew Snowden
Draisma recently proved that polynomial representations of are topologically noetherian. We generalize this result to algebraic representations of infinite r…
Topological noetherianity for cubic polynomials
Harm Derksen, Rob H. Eggermont, Andrew Snowden
Let be the space of complex cubic polynomials in infinitely many variables. We show that this space is -noetherian, meaning that an…
Regular maps of high density
R. H. Eggermont, M. Hendriks
A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection…
Algebraic boundary of matrices of nonnegative rank at most three
Rob H. Eggermont, Emil Horobet, Kaie Kubjas
The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component.…
Finiteness properties of congruence classes of infinite matrices
Rob Eggermont
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of t…
Plücker varieties and higher secants of Sato's Grassmannian
Jan Draisma, Rob H. Eggermont
Every Grassmannian, in its Plücker embedding, is defined by quadratic polynomials. We prove a vast, qualitative, generalisation of this fact to what we call Plücker varieties. A Pl…
Noetherianity for infinite-dimensional toric varieties
Jan Draisma, Rob H. Eggermont, Robert Krone +1
We consider a large class of monomial maps respecting an action of the infinite symmetric group, and prove that the toric ideals arising as their kernels are finitely generated up…
Finiteness results for Abelian tree models
Jan Draisma, Rob H. Eggermont
Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant refers to a symmetry group imposed on the root d…