1 citations · 1 across the 8 of their papers we have counts for
9 papers
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…
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…
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…
From Feynman diagrams to the amplituhedron: a gentle review
Shounak De, Dmitrii Pavlov, Marcus Spradlin +1
In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail, in order to bridge the gap in understa…
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…