40 citations · 460 across the 64 of their papers we have counts for
7 papers · 1 filter
Geometry of the Gaussian graphical model of the cycle
Rodica Andreea Dinu, Mateusz Michałek, Martin Vodička
We prove a conjecture due to Sturmfels and Uhler concerning the degree of the projective variety associated to the Gaussian graphical model of the cycle. We involve new methods bas…
Applications of intersection theory: from maximum likelihood to chromatic polynomials
Rodica Andreea Dinu, Mateusz Michałek, Tim Seynnaeve
Recently, we have witnessed tremendous applications of algebraic intersection theory to branches of mathematics, that previously seemed very distant. In this article we review some…
Characteristic numbers and chromatic polynomial of a tensor
Austin Conner, Mateusz Michałek
We introduce the characteristic numbers and the chromatic polynomial of a tensor. Our approach generalizes and unifies the chromatic polynomial of a graph and of a matroid, charact…
Equations for GL invariant families of polynomials
Paul Breiding, Christian Ikenmeyer, Mateusz Michałek +1
We provide an algorithm that takes as an input a given parametric family of homogeneous polynomials, which is invariant under the action of the general linear group, and an integer…
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…
Ideals of Spaces of Degenerate Matrices
Julian Vill, Mateusz Michałek, Alexander Taveira Blomenhofer
The variety consists of all tuples of matrices such that every linear combination of is singula…
Bounds on complexity of matrix multiplication away from CW tensors
Roser Homs, Joachim Jelisiejew, Mateusz Michałek +1
We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, or monomial algebras. We analyse them using Strassen's laser m…