4 citations · 10 across the 6 of their papers we have counts for
9 papers
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…
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…
Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming
Laurent Manivel, Mateusz Michałek, Leonid Monin +2
We establish connections between: the maximum likelihood degree (ML-degree) for linear concentration models, the algebraic degree of semidefinite programming (SDP), and Schubert ca…
Reciprocal maximum likelihood degrees of diagonal linear concentration models
Christopher Eur, Tara Fife, José Alejandro Samper +1
We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model of dimension is equal to $(-2)^rχ_M( \…
K-theoretic Tutte polynomials of morphisms of matroids
Rodica Dinu, Christopher Eur, Tim Seynnaeve
We generalize the Tutte polynomial of a matroid to a morphism of matroids via the K-theory of flag varieties. We introduce two different generalizations, and demonstrate that each…
The Hessian Discriminant
Rodica Dinu, Tim Seynnaeve
We express the Hessian discriminant of a cubic surface in terms of fundamental invariants. This answers Question 15 from the \emph{27 questions on the cubic surface}. We also expla…
Uniform matrix product states from an algebraic geometer's point of view
Adam Czapliński, Mateusz Michałek, Tim Seynnaeve
We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equ…
A tensor version of the quantum Wielandt theorem
Mateusz Michałek, Tim Seynnaeve, Frank Verstraete
We prove boundedness results for the injectivity regions for PEPS. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.
Flag matroids: algebra and geometry
Amanda Cameron, Rodica Dinu, Mateusz Michałek +1
Matroids are ubiquitous in modern combinatorics. As discovered by Gelfand, Goresky, MacPherson and Serganova there is a beautiful connection between matroid theory and the geometry…