相关论文: Positroids, Plabic Graphs, and Scattering Amplitud…
We investigate properties of four point colour ordered scattering amplitudes in D=6 fishnet CFT. We show that such amplitudes are related via very simple relation to their D=4 counterparts considered previously in the literature. Exploiting…
Shelling orders are a ubiquitous tool used to understand invariants of cell complexes. Significant effort has been made to develop techniques to decide when a given complex is shellable. However, empirical evidence shows that some shelling…
This note is a complete library of symbolic parametrized expressions for both real and complexified configuration spaces of a planar 4-bar linkage. Building upon the previous work from Izmestiev (2015), this library expands on the…
In this note I will explain how relative/log Gromov-Witten invariants of pairs $(X,D)$ with very ample smooth anticanonical divisor $D$ can be computed using algebro-combinatorial objects called scattering diagrams. The underlying principle…
In this article we review some problems in physics, chemistry and mathematics that lead naturally to a class of polyhedra which include the Platonic solids. Examples include the study of electrons on a sphere, cages of carbon atoms, central…
The suite of highly confined polaritons supported by two-dimensional (2D) materials constitutes a versatile platform for nano-optics, offering the means to channel light on deep-subwavelength scales. Graphene, in particular, has attracted…
We review recent progress in Bipartite Field Theories. We cover topics such as their gauge dynamics, emergence of toric Calabi-Yau manifolds as master and moduli spaces, string theory embedding, relationships to on-shell diagrams,…
This report shows formulation of wave scattering in frequency domain. The formulation provides an understanding of S-matrix solver which is named as Scattering Matrix Analyzer (SMatrAn). The S-matrix has the whole of amplitude and phase…
Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural properties. We investigate the use of spectral sparsification to produce good visual…
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…
The classical volume polynomial in algebraic geometry measures the degrees of ample (and nef) divisors on a smooth projective variety. We introduce an analogous volume polynomial for matroids, and give a complete combinatorial formula. For…
A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying $\mathcal{PT}$-symmetry. It is illustrated that unlike in…
Particle scattering is a powerful tool to unveil the nature of various subatomic phenomena. The key quantity is the scattering amplitude whose analytic structure carries the information of the quantum states. In this work, we demonstrate…
Given a homogeneous ideal $I$ in a polynomial ring over a field, one may record, for each degree $d$ and for each polynomial $f\in I_d$, the set of monomials in $f$ with nonzero coefficients. These data collectively form the tropicalization…
We continue the study of positive geometries underlying the {\it Grassmannian string integrals}, which are a class of "stringy canonical forms", or stringy integrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. The…
At the tree level, the scattering processes involving open and closed strings are described by a disk world-sheet with vertex operator insertions at the boundary and in the bulk. Such amplitudes can be decomposed as certain linear…
Compound resonances in nucleon-nucleus scattering are related to the discrete spectrum of the target. Such resonances can be studied in a unified and general framework by a scattering model that uses sturmian expansions of postulated…
Using Postnikov's Le-diagrams, decorated permutations, and Grassmann necklaces, we classify which positroids are sparse paving matroids. This allows us to enumerate sparse paving positroids, making connections to a known sequence involving…
Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…
We propose a plasmonic device consisting of a concentric ring grating acting as an efficient tool for directional launching and detection of surface plasmon-polaritons (SPPs). Numerical simulations and optical characterizations are used to…