21 citations · 210 across the 36 of their papers we have counts for
38 papers
Schubert compactifications of matrix pencils
Vincenzo Galgano, Fulvio Gesmundo, Hanieh Keneshlou
The Schubert compactification of a linear space of matrices is a natural compactification of in the Grassmannian . T…
Computing the continuous symmetries of a parametrized variety
Benjamin Biaggi, Jan Draisma, Fulvio Gesmundo +2
We prove that the symmetry Lie algebra of a parametrized variety can be determined directly from the parametrization, without computing the vanishing ideal of the variety. We deriv…
Triangular tensor networks, pencils of matrices and beyond
Alessandra Bernardi, Fulvio Gesmundo
We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors…
Marvelous slices of orthogonal matrices
Taylor Brysiewicz, Fulvio Gesmundo
The space of special orthogonal matrices with zeros on the diagonal decomposes into the union of irreducible surfaces whose intersections are beautifully encoded…
Polynomials of small slice rank and strength
Cosimo Flavi, Fulvio Gesmundo, Alessandro Oneto +1
This paper investigates defining equations for secant varieties of the variety of reducible polynomials, which geometrically encode the notions of strength and slice rank of homoge…
Linear preservers of secant varieties and other varieties of tensors
Fulvio Gesmundo, Young In Han, Benjamin Lovitz
We study the problem of characterizing linear preserver subgroups of algebraic varieties, with a particular emphasis on secant varieties and other varieties of tensors. We introduc…
Collineation varieties of tensors
Fulvio Gesmundo, Hanieh Keneshlou
In this article, we introduce the -th collineation variety of a third order tensor. This is the closure of the image of the rational map of size minors of a matrix of linear…
Quatroids and Rational Plane Cubics
Taylor Brysiewicz, Fulvio Gesmundo, Avi Steiner
It is a classical result that there are (irreducible) rational cubic curves through generic points in , but little is known about the non-generi…
Characteristic polynomials and eigenvalues of tensors
Francesco Galuppi, Fulvio Gesmundo, Ettore Teixeira Turatti +1
We lay the geometric foundations for the study of the characteristic polynomial of tensors. For symmetric tensors of order and dimension , and symmetric tensors of or…
The next gap in the subrank of 3-tensors
Fulvio Gesmundo, Jeroen Zuiddam
Recent works of Costa-Dalai, Christandl-Gesmundo-Zuiddam, Blatter-Draisma-Rupniewski, and Briët-Christandl-Leigh-Shpilka-Zuiddam have investigated notions of discreteness and gaps…
Hilbert Functions of Chopped Ideals
Fulvio Gesmundo, Leonie Kayser, Simon Telen
A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite s…
Geometry of Tensors: Open problems and research directions
Fulvio Gesmundo
This is a collection of open problems and research ideas following the presentations and the discussions of the AGATES Kickoff Workshop held at the Institute of Mathematics of the…
Decompositions and Terracini loci of cubic forms of low rank
Luca Chiantini, Fulvio Gesmundo
We study Waring rank decompositions for cubic forms of rank in variables. In this setting, we prove that if a concise form has more than one non-redundant decomposition…
Partial Degeneration of Tensors
Matthias Christandl, Fulvio Gesmundo, Vladimir Lysikov +1
Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor fact…
A Gap in the Subrank of Tensors
Matthias Christandl, Fulvio Gesmundo, Jeroen Zuiddam
The subrank of tensors is a measure of how much a tensor can be ''diagonalized''. This parameter was introduced by Strassen to study fast matrix multiplication algorithms in algebr…
Geometric complexity theory for product-plus-power
Pranjal Dutta, Fulvio Gesmundo, Christian Ikenmeyer +2
According to Kumar's recent surprising result (ToCT'20), a small border Waring rank implies that the polynomial can be approximated as a sum of a constant and a small product of li…
Degree-restricted strength decompositions and algebraic branching programs
Fulvio Gesmundo, Purnata Ghosal, Christian Ikenmeyer +1
We analyze Kumar's recent quadratic algebraic branching program size lower bound proof method (CCC 2017) for the power sum polynomial. We present a refinement of this method that g…
The Geometry of Discotopes
Fulvio Gesmundo, Chiara Meroni
We study a class of semialgebraic convex bodies called discotopes. These are instances of zonoids, objects of interest in real algebraic geometry and random geometry. We focus on t…
Algebraic compressed sensing
Paul Breiding, Fulvio Gesmundo, Mateusz Michałek +1
We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for i…
Dimension of Tensor Network varieties
Alessandra Bernardi, Claudia De Lazzari, Fulvio Gesmundo
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on…
Border rank non-additivity for higher order tensors
Matthias Christandl, Fulvio Gesmundo, Mateusz Michałek +1
Whereas matrix rank is additive under direct sum, in 1981 Schönhage showed that one of its generalizations to the tensor setting, tensor border rank, can be strictly subadditive fo…
Optimization at the boundary of the tensor network variety
Matthias Christandl, Fulvio Gesmundo, Daniel Stilck Franca +1
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying…
The Degree of Stiefel Manifolds
Taylor Brysiewicz, Fulvio Gesmundo
We compute the degree of Stiefel manifolds, that is, the variety of orthonormal frames in a finite dimensional vector space. Our approach employs techniques from classical algebrai…
Tensors with maximal symmetries
Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +1
We classify tensors with maximal and next to maximal dimensional symmetry groups under a natural genericity assumption (1-genericity), in dimensions greater than 7. In other words,…