相关论文: Amplituhedra and origami
We glue two manifolds which have curvature operators at least k (in the sense of eigenvalues) along their common boundary. We show that if the sum of the second fundamental forms of the boundary is positive semidefinite, then the curvature…
We introduce $\mathcal{B}_{\kappa}$-embeddings, nonlinear mathematical structures that connect, through smooth paths parameterized by $\kappa$, a finite or denumerable set of objects at $\kappa=0$ (e.g. numbers, functions, vectors,…
The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and…
We map the problem of determining flat-foldability of the origami diagram onto the ground-state search problem of spin glass model on random graphs. If the origami diagram is locally flat-foldable around each vertex, a pre-folded diagram,…
Let $\Gamma$ be a dual polar graph with diameter $D \geqslant 3$, having as vertices the maximal isotropic subspaces of a finite-dimensional vector space over the finite field $\mathbb{F}_q$ equipped with a non-degenerate form (alternating,…
We solve the Einstein equations in higher dimensions with warped geometry where an extra dimension is assumed to have orbifold symmetry $S^{1}/Z_{2}$. The setup considered here is an extension of the five-dimensional Randall-Sundrum model…
Oscillating shapes of the primordial bispectrum are present in many inflationary models. The Planck experiment has recently published measurements of oscillating shapes, which were however limited to the efficient frequency range of the…
In this note, using Nekrasov's gauge origami framework, we study two different versions of the the BPS/CFT correspondence - first, the standard AGT duality and, second, the quiver W algebra construction which has been developed recently by…
The positive Grassmannian $Gr_{k,n}^{\geq 0}$ is the subset of the real Grassmannian where all Pl\"ucker coordinates are nonnegative. It has a beautiful combinatorial structure as well as connections to statistical physics, integrable…
We find a family of planar bipartite graphs all of whose Lombardi drawings (drawings with circular arcs for edges, meeting at equal angles at the vertices) are nonplanar. We also find families of embedded series-parallel graphs and…
We characterize the bialgebraic varieties of the $\Gamma$ function, that is, if $V,W\subseteq\mathbb{C}^n$ are irreducible affine algebraic variety which satisfy $\dim V =\dim W$ and $\Gamma(V)\subseteq W$, then the equations defining $V$…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
We consider embeddings of 3-regular graphs into 3-dimensional Cartesian coordinates, in such a way that two vertices are adjacent if and only if two of their three coordinates are equal (that is, if they lie on an axis-parallel line) and…
We estimate whether there is an embedding from one n-dimensional rectangle into another which expands every k-dimensional area. Our estimate is sharp up to a constant factor in each dimension.
We study the pressure of the "edge-triangle model", which is equivalent to the cumulant generating function of triangles in the Erd\"os-R\'enyi random graph. By analyzing finite graphs of increasing volume, as well as the graphon…
We found an explicit description of all $GL(n,\RR)$-Whittaker functions as oscillatory integrals and thus constructed equivariant mirrors of flag manifolds. As a consequence we proved the Virasoro conjecture for flag manifolds.
In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into $L_1$. As a corollary, we obtain that all planar graphs which are 1-skeletons of planar non-positively…
In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization.…
Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The…
We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza-Klein)…