6 papers · 1 filter
Positive Genus Pairs from Amplituhedra
Joris Koefler, Dmitrii Pavlov, Rainer Sinn
A main conjecture in the field of Positive Geometry states that amplituhedra, which are certain semi-algebraic sets in the Grassmannian, are positive geometries. It is motivated by…
Positive Polytopes with Few Facets in the Grassmannian
Dmitrii Pavlov, Kristian Ranestad
In this article we study adjoint hypersurfaces of geometric objects obtained by intersecting simple polytopes with few facets in with the Grassmannian $\mathrm{Gr}(2…
Parke-Taylor varieties
Benjamin Hollering, Dmitrii Pavlov
Parke-Taylor functions are certain rational functions on the Grassmannian of lines encoding MHV amplitudes in particle physics. For particles there are Parke-Taylor functi…
Adjoints of Polytopes: Determinantal Representations and Smoothness
Clemens Brüser, Mario Kummer, Dmitrii Pavlov
In this article we study determinantal representations of adjoint hypersurfaces of polytopes. We prove that adjoint polynomials of all polygons can be represented as determinants o…
Hyperplane Arrangements in the Grassmannian
Elia Mazzucchelli, Dmitrii Pavlov, Kexin Wang
The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the G…
Santaló Geometry of Convex Polytopes
Dmitrii Pavlov, Simon Telen
The Santaló point of a convex polytope is the interior point which leads to a polar dual of minimal volume. This minimization problem is relevant in interior point methods for con…