1 citations · 1 across the 9 of their papers we have counts for
11 papers
Degenerating Discriminants
Viktoriia Borovik, Clara Briand
We study the behavior of projective dual varieties and discriminants under flat degenerations. For Gröbner degenerations, we show that the conormal variety admits a Gröbner degener…
Constraining Conformal Correlators
Viktoriia Borovik, Claire de Korte, Nathan Meurrens +1
We study the space of conformally covariant -point functions of spinning operators using methods from invariant theory, commutative algebra, and combinatorics. We show that the…
Elimination ideals of Plücker ideals and algebras with straightening laws
Viktoriia Borovik, Takayuki Hibi
It is well known that the Plücker ideal defining the Grassmannian is generated by quadratic Plücker relations. These relations form a reverse lexicographic Gröbner basis and endow…
Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties
Viktoriia Borovik, Hannah Friedman, Serkan Hoşten +1
We study energy minimization problems in quantum chemistry through the lens of computational algebraic geometry. We focus on minimizing the Rayleigh quotient of a Hamiltonian over…
Graphical Scattering Equations
Barbara Betti, Viktoriia Borovik, Bella Finkel +2
The CHY scattering equations on the moduli space play a prominent role at the interface of particle physics and algebraic statistics. We study the scattering corresponden…
On the construction of a counterexample to Strassen's rank additivity conjecture
Viktoriia Borovik, Cosimo Flavi, Paweł Pielasa +2
The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individu…
The SagbiHomotopy.jl package for solving polynomial systems
Barbara Betti, Viktoriia Borovik
We present the Julia package SagbiHomotopy.jl for solving systems of polynomial equations using numerical homotopy continuation. The package introduces an optimal choice of a start…
Proudfoot-Speyer degenerations of scattering equations
Barbara Betti, Viktoriia Borovik, Simon Telen
We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as lin…
Additive actions on projective hypersurfaces with a finite number of orbits
Viktoriia Borovik, Alexander Chernov, Anton Shafarevich
An induced additive action on a projective variety is a regular action of the group on with an open orbit, which can be extended to…
SAGBI and Gröbner Bases Detection
Viktoriia Borovik, Timothy Duff, Elima Shehu
We introduce a detection algorithm for SAGBI basis in polynomial rings, analogous to a Gröbner basis detection algorithm previously proposed by Gritzmann and Sturmfels. We also pre…
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…