6 papers
Degree of tensor train varieties via integral geometry
Andrea Rosana, Otto T. P. Schmidt
In this work we consider tensor train varieties. These are varieties of tensors arising in a range of fields, including quantum many-body physics and machine learning. Using method…
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 3…
Distance Optimization in the Grassmannian of Lines
Hannah Friedman, Andrea Rosana, Bernd Sturmfels
The square of a skew-symmetric matrix is a symmetric matrix whose eigenvalues have even multiplicities. When the matrices have rank two, they represent the Grassmannian of lines, a…
What is the probability that a random symmetric tensor is close to rank-one?
Alberto Cazzaniga, Antonio Lerario, Andrea Rosana
We address the general problem of estimating the probability that a real symmetric tensor is close to rank-one tensors. Using Weyl's tube formula, we turn this question into a diff…
The Grassmann distance complexity
Antonio Lerario, Andrea Rosana
Motivated by the concept of Euclidean Distance Degree, which measures the complexity of finding the nearest point to an algebraic set in Euclidean space, we introduce the notion of…
Typical ranks of random order-three tensors
Paul Breiding, Sarah Eggleston, Andrea Rosana
In this paper we study typical ranks of real tensors. In the case the typical ranks are contained in ,…