1 citations · 3 across the 9 of their papers we have counts for
9 papers
Log Canonical Models and Positive Geometries
Benjamin Hollering, Dmitrii Pavlov, Elizabeth Pratt
Constructing log canonical compactifications of open varieties is a central problem in birational geometry. Finding a natural coordinate system and obtaining the equations of these…
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…
Algebraic Geometry of Quantum Graphical Models
Eliana Duarte, Dmitrii Pavlov, Maximilian Wiesmann
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study…
Combinatorics of Grasstopes
Yelena Mandelshtam, Dmitrii Pavlov, Elizabeth Pratt
A Grasstope is the image of the totally nonnegative Grassmannian under a linear map . This is a generaliza…
On real and observable rational realizations of input-output equations
Sebastian Falkensteiner, Dmitrii Pavlov, Rafael Sendra
Given a single (differential-algebraic) input-output equation, we present a method for finding different representations of the associated system in the form of rational realizatio…
Logarithmically Sparse Symmetric Matrices
Dmitrii Pavlov
A positive definite matrix is called logarithmically sparse if its matrix logarithm has many zero entries. Such matrices play a significant role in high-dimensional statistics and…
Gibbs Manifolds
Dmitrii Pavlov, Bernd Sturmfels, Simon Telen
Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum~physics, where…
On realizing differential-algebraic equations by rational dynamical systems
Dmitrii Pavlov, Gleb Pogudin
Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only…
From algebra to analysis: new proofs of theorems by Ritt and Seidenberg
Dmitrii Pavlov, Gleb Pogudin, Yury Razmyslov
Ritt's theorem of zeroes and Seidenberg's embedding theorem are classical results in differential algebra allowing to connect algebraic and model-theoretic results on nonlinear PDE…