相关论文: Computation of Gross-Keating invariants

In this paper, based on techniques of Newton polygons, a result which allows the computation of a p integral basis of every quartic number field is given. For each prime integer p, this result allows to compute a p-integral basis of a…

A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…

This paper wishes to foster communication between mathematicians and physicists working in mirror symmetry and orbifold Gromov-Witten theory. We provide a reader friendly review of the physics computation in [arXiv:hep-th/0607100] that…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

We survey connections of the Grothendieck inequality and its variants to combinatorial optimization and computational complexity.

We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand. The…

Gromov-Witten invariants of a symplectic manifold are a count of holomorphic curves. We describe a formula expressing the GW invariants of a symplectic sum $X# Y$ in terms of the relative GW invariants of $X$ and $Y$. This formula has…

Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…

We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.

Runge's method is a tool to figure out integral points on curves effectively in terms of height. This method has been generalised to varieties of any dimension, unfortunately its conditions of application are often too restrictive. In this…

Let G be a connected reductive group. In this paper we are studying the invariant theory of symplectic G-modules. Our main result is that the invariant moment map is equidimensional. We deduce that the categorical quotient is a fibration…

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms…

The Kac-Ward formula allows to compute the Ising partition function on a planar graph G with straight edges from the determinant of a matrix of size 2N, where N denotes the number of edges of G. In this paper, we extend this formula to any…

We introduce a new approach to universal quantum knot invariants that emphasizes generating functions instead of generators and relations. All the relevant generating functions are shown to be perturbed Gaussians of the form $Pe^G$, where…

Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…

We determine explicitly the Gauss sums on the general linear group $GL_2(\mathbb{Z}/p^l\mathbb{Z})$ for all irreducible characters, where $p$ is an odd prime and $l$ is an integer > 1. While there are several studies of the Gauss sums on…

We investigate the complex reflection group $\mathfrak{G}$ associated with the octahedral group, identified as the ninth entry in the Shephard-Todd classification. We determine all irreducible representations of $\mathfrak{G}$ and compute…

When $G$ is a complex reductive algebraic group and $G/K$ is a reductive symmetric space, the decomposition of $\C[G/K]$ as a $K$-module was obtained (in a non-constructive way) by Richardson, generalizing the celebrated result of…

We improve the bound of the $g$-invariant of the ring of integers of a totally real number field, where the $g$-invariant $g(r)$ is the smallest number of squares of linear forms in $r$ variables that is required to represent all the…

We survey recent contributions to finite element exterior calculus on manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differential equations on manifolds. Our primary focus is on…