5 citations · 6 across the 10 of their papers we have counts for
10 papers
Border rank=rank for Kruskal tensors and a Kruskal's theorem for skew decompositions
Alexander Taveira Blomenhofer, Benjamin Lovitz
We show that border rank is equal to rank for Kruskal tensors. We also give an analogous Kruskal condition for alternating tensors, which certifies uniqueness of skew rank decompos…
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the t…
A linear-time algorithm for Chow decompositions
Alexander Taveira Blomenhofer, Benjamin Lovitz
We propose a linear-time algorithm to compute low-rank Chow decompositions. Our algorithm can decompose concise symmetric 3-tensors in n variables of Chow rank n/3. The algorithm i…
On defectivity of joins, reducible secants and Fröberg's conjecture
Alexander Blomenhofer, Alex Casarotti
We introduce the notion of r-defectivity for a vector bundle on a quasi-projective variety. Using this tool, we prove several previously unknown cases of Fröberg's conjecture and a…
Moment-sos and spectral hierarchies for polynomial optimization on the sphere and quantum de Finetti theorems
Alexander Taveira Blomenhofer, Monique Laurent
We revisit the convergence analysis of two approximation hierarchies for polynomial optimization on the unit sphere. The first one is based on the moment-sos approach and gives sem…
Nondefectivity of invariant secant varieties
Alexander Taveira Blomenhofer, Alex Casarotti
We show that a large class of secant varieties is nondefective. In particular, we positively resolve most cases of the Baur-Draisma-de Graaf conjecture on Grassmannian secants in l…
Gaussian Mixture Identifiability from degree 6 Moments
Alexander Taveira Blomenhofer
We resolve most cases of identifiability from sixth-order moments for Gaussian mixtures on spaces of large dimensions. Our results imply that the parameters of a generic mixture of…
Unique powers-of-forms decompositions from simple Gram spectrahedra
Alexander Taveira Blomenhofer
We consider simultaneous Waring decompositions: Given forms of degrees , , which admit a representation as -th power sums of -forms $ q_1,\ldot…
Identifiability for mixtures of centered Gaussians and sums of powers of quadratics
Alexander Taveira Blomenhofer, Alex Casarotti, Alessandro Oneto +1
We consider the inverse problem for the polynomial map which sends an -tuple of quadratic forms in variables to the sum of their -th powers. This map captures the moment…
A new Algorithm for Overcomplete Tensor Decomposition based on Sums-of-Squares Optimisation
Alexander Taveira Blomenhofer
In this thesis, a new class of algorithms based on Sums of Squares Programming is developed. These allow to reduce a degree- homogeneous polynomial $T = \sum_{i = 1}^m \langle a…