Related papers: The Chirotropical Grassmannian
Here we give brief account of hermitian symplectic spaces, showing that they are intimately connected to symmetric as well as self-adjoint extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange…
In this thesis we study the relation between scattering diagrams and deformations of holomorphic pairs, building on a recent work of Chan--Conan Leung--Ma. The new feature is the extended tropical vertex group where the scattering diagrams…
We give a conjectural formula for sheaves supported on (irreducible) conormal varieties inside the cotangent bundle of the Grassmannian, such that their equivariant $K$-class is given by the partition function of an integrable loop model,…
Following a formula found in the paper of Avramov, Iyengar, Lipman, and Nayak (2010) and ideas of Neeman and Khusyairi, we indicate that Grothendieck duality for finite tor-amplitude maps can be developed from scratch via the formula $f^!…
We study the topological-antitopological fusion equations for supersymmetric sigma models on Grassmannian manifolds G(k,N). We find a basis in which the metric becomes diagonal and the $tt^*$ equations become tractable. The solution for the…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
In this paper we study the role of planarity in generalized scattering amplitudes, through several closely interacting structures in combinatorics, algebraic and tropical geometry. The generalized biadjoint scalar amplitude, introduced…
Let $n,k$ denote integers with $n>2k\geq 6$. Let $\mathbb{F}_q$ denote a finite field with $q$ elements, and let $V$ denote a vector space over $\mathbb{F}_q$ that has dimension $n$. The projective geometry $P_q(n)$ is the partially ordered…
Let F* be the field of q elements and let P(n,q) denote the projective space of dimension n-1 over F*. We construct a family H^{n}_{k,i} of combinatorial homology modules associated to P(n,q) for a coefficient field F of positive…
We define affine growth diagrams consisting of $GL_m$ dominant weights that label the vertices of a staircase-shaped grid. These are also called cylindrical growth diagrams as defined by Speyer and White in the case of partitions. The…
Following the ideas of Bossinger and Fang, Fourier, and Littelman, we study iterated sequences for the Grassmannian $\operatorname{Gr} (3, n)$ as a special class of birational sequences. For each iterated sequence $S$, there is a weighting…
A large family of nonsingular rational solutions of the Kadomtsev-Petviashvili (KP) I equation are investigated. These solutions are constructed via the Gramian method and are identified as points in a complex Grassmannian. Each solution is…
We construct an explicit, embedded degeneration of the general torus orbit closure in the maximal orthogonal Grassmannian OG(n,2n+1) into a union of Richardson varieties. In particular, we deduce a formula for the cohomology class of the…
Projective embedding of an isotropic Grassmannian (or pure spinors) OGr^+(5,10) into projective space of spinor representation S can be characterized with a help of Gamma-matrices by equations Gamma_{alpha…
We extend vector configurations to more general objects that have nicer combinatorial and topological properties, called weighted pseudosphere arrangements. These are defined as a weighted variant of arrangements of pseudospheres, as in the…
We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\sigma$-moduli multivariate polynomial of what we call the $\textit{standard form}$. We show that a…
We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of…
The tropical variety of a $d$-dimensional prime ideal in a polynomial ring with complex coefficients is a pure $d$-dimensional polyhedral fan. This fan is shown to be connected in codimension one. We present algorithmic tools for computing…
We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as…
We describe basic diffeological structures related to splittings and Grassmannians for infinite dimensional vector spaces. We analyze and expand the notion of non-commutative cross-ratio and prove its smoothness. Then we illustrate this…