4 citations · 10 across the 9 of their papers we have counts for
11 papers
Eigenvector Varieties
Sandra Di Rocco, Bernd Sturmfels, Svala Sverrisdóttir
Any linear space of square matrices has an associated eigenvector variety. Its points are eigenvectors of matrices from that linear space. We present a systematic study of eigenvec…
Gram Matrices for Isotropic Vectors
Yassine El Maazouz, Bernd Sturmfels, Svala Sverrisdóttir
We investigate determinantal varieties for symmetric matrices that have zero blocks along the main diagonal. In theoretical physics, these arise as Gram matrices for kinematic vari…
Kinematic Varieties for Massless Particles
Smita Rajan, Svala Sverrisdóttir, Bernd Sturmfels
We study algebraic varieties that encode the kinematic data for massless particles in -dimensional spacetime subject to momentum conservation. Their coordinates are spinor b…
The Two Lives of the Grassmannian
Karel Devriendt, Hannah Friedman, Bernhard Reinke +1
The real Grassmannian is both a projective variety (via Plücker coordinates) and an affine variety (via orthogonal projections). We connect these two representations, and we develo…
Coupled Cluster Degree of the Grassmannian
Viktoriia Borovik, Bernd Sturmfels, Svala Sverrisdóttir
We determine the number of complex solutions to a nonlinear eigenvalue problem on the Grassmannian in its Plücker embedding. This is motivated by quantum chemistry, where it repres…
Algebraic Varieties in Quantum Chemistry
Fabian Faulstich, Bernd Sturmfels, Svala Sverrisdóttir
We develop algebraic geometry for coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schrödinger equation…
Likelihood Geometry of Determinantal Point Processes
Hannah Friedman, Bernd Sturmfels, Maksym Zubkov
We study determinantal point processes (DPP) through the lens of algebraic statistics. We count the critical points of the log-likelihood function, and we compute them for small mo…
Tropical Implicitization Revisited
Kemal Rose, Bernd Sturmfels, Simon Telen
Tropical implicitization means computing the tropicalization of a unirational variety from its parametrization. In the case of a hypersurface, this amounts to finding the Newton po…
Positive del Pezzo Geometry
Nick Early, Alheydis Geiger, Marta Panizzut +2
Real, complex, and tropical algebraic geometry join forces in a new branch of mathematical physics called positive geometry. We develop the positive geometry of del Pezzo surfaces…
Taylor Polynomials of Rational Functions
Aldo Conca, Simone Naldi, Giorgio Ottaviani +1
A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one va…
Moment Varieties for Mixtures of Products
Yulia Alexandr, Joe Kileel, Bernd Sturmfels
The setting of this article is nonparametric algebraic statistics. We study moment varieties of conditionally independent mixture distributions on . These are the sec…