Related papers: Septic equations are solvable by 2-fold origami
We classify solvable Lie groups admitting left invariant symplectic half-flat structure. When the Lie group has a compact quotient by a lattice, we show that these structures provide solutions of supersymmetric equations of type IIA.
Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The $\mathcal{N}=1$ superconformal algebra is extended by additional generators of…
We present a method to obtain higher order integrals and polynomial algebras for two-dimensional superintegrable systems from creation and annihilation operators. All potentials with a second and a third order integrals of motion separable…
We describe an efficient algorithm which, given a principally polarized (p.p.) abelian surface $A$ over $\mathbb{Q}$ with geometric endomorphism ring equal to $\mathbb{Z}$, computes all the other p.p. abelian surfaces over $\mathbb{Q}$ that…
We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the twenty-five octic fields with Galois…
In this paper the elliptic genus for a general Calabi-Yau fourfold is derived. The recent work of Kawai calculating N=2 heterotic string one-loop threshold corrections with a Wilson line turned on is extended to a similar computation where…
We classify all closed non-orientable P2-irreducible 3-manifolds with complexity up to 7, fixing two mistakes in our previous complexity-up-to-6 classification. We show that there is no such manifold with complexity less than 6, five with…
We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class of rational functions generalizing the classical Redei…
We study parameterized elliptic systems on symmetric domains with additional system symmetries. We prove the existence of continua of nontrivial solutions bifurcating from the constant branch determined by a critical point of the potential,…
In this paper we show that it is possible to project onto the solutions of the $\mathfrak{grt}$ hexagon equation. We also consider in some sense generalized hexagon equations and other symmetry equations for multiple argument maps between…
We consider a class of fully nonlinear second order elliptic equations on Hermitian manifolds closely related to the general notion of $\bfG$-plurisubharmonicity of Harvey-Lawson and an equation treated by Sz\'ekelyhidi-Tosatti-Weinkove in…
Let $S$ be an abelian surface over an algebraically closed field $k$ with characteristic different from $2$ and $3$, and $\mathcal{L}$ a symmetric ample line bundle defining a polarisation of type $(1,3)$. Then the linear system…
A toric origami manifold is a generalization of a symplectic toric manifold (or a toric symplectic manifold). The origami symplectic form is allowed to degenerate in a good controllable way in contrast to the usual symplectic form. It is…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross…
A formalism is given to count integer and rational solutions to polynomial equations with rational coefficients. These polynomials $P(x)$ are parameterized by three integers, labeling an elliptic curve. The counting of the rational…
In 1967, Shioda \cite{Shi1} determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined in \cite{Shi1} are incorrect. In this paper, we compute the correct…
We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully…
The radical solution of polynomials with rational coefficients is a famous solved problem. This paper found that it is a $\mathbb{NP}$ problem. Furthermore, this paper found that arbitrary $ \mathscr{P} \in \mathbb{P}$ shall have a one-way…
We apply a symbolic approach of the general quadratic decomposition of polynomial sequences - presented in a previous article referenced herein - to polynomial sequences fulfilling specific orthogonal conditions towards two given…