Related papers: Configurations of points with sum 0
We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincar\'e inequality holds. We show that the constant rank condition is sufficient. The concept of the…
Starting with the first-order singular Lagrangian, the canonical structures of the noncommutative quantum system on a submanifold embedded in the higher-dimensional Euclidean space are investigated with the projection operator method (POM)…
Let $E$ be an elliptic curve of conductor $N$, and let $K$ be an imaginary quadratic field such that the root number of $E/K$ is $-1$. Let $O$ be an order in $K$ and assume that there exists an odd prime $p$, such that $p^2 \mid\mid N$, and…
We present some methods for constructing connected spatial geometric configurations $(p_{q}, n_{k})$ of points and lines, preserved by the same rotations (and reflections) of Euclidean space $E^{3}$ as the chosen Platonic solid. In this…
We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We start by providing a hybrid numeric-symbolic…
We present an efficient algorithm for calculating the number of components of an integral lamination on an $n$-punctured disk, given its Dynnikov coordinates. The algorithm requires $O(n^2M)$ arithmetic operations, where $M$ is the sum of…
In this paper, we generalize the results presented in [5] for the case of real algebraic space curves. More precisely, given an algebraic space curve C (parametrically or implicitly defined), we show how to compute the generalized…
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…
Stable quotient spaces provide an alternative to stable maps for compactifying spaces of maps. When the target is projective space and the domain curve has genus 1, these are smooth proper Deligne-Mumford stacks. In this paper we study the…
In [DKO] we constructed virtual fundamental classes $[[ Hilb^m_V ]]$ for Hilbert schemes of divisors of topological type m on a surface V, and used these classes to define the Poincare invariant of V: (P^+_V,P^-_V): H^2(V,Z) --> \Lambda^*…
We report on an implementation of Galois groups in the new computer algebra system OSCAR. As an application we compute Galois groups of Ehrhart polynomials of lattice polytope
We study certain generic systems of real polynomial equations associated with triangulations of convex polytopes and investigate their number of real solutions. Our main focus is set on pairs of plane algebraic curves which form a so-called…
We derive an identity for certain linear combinations of polylogarithm functions with negative exponents, which implies relations for linear combinations of Eulerian numbers. The coefficients of our linear combinations are related to…
We study the structure of collections of algebraic curves in three dimensions that have many curve-curve incidences. In particular, let $k$ be a field and let $\mathcal{L}$ be a collection of $n$ space curves in $k^3$, with…
We describe a provably quasi-polynomial algorithm to compute discrete logarithms in the multiplicative groups of finite fields of small characteristic, that is finite fields whose characteristic is logarithmic in the order. We partially…
Given an absolutely irreducible ternary form $F$, the purpose of this paper is to produce better upper bounds for the number of integer solutions to the equation F=0, that are restricted to lie in very lopsided boxes. As an application of…
We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (i) wireless…
Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…
We give bounds for exponential sums over curves defined over Galois rings. We first define summation subsets as the images of lifts of points from affine opens of the reduced curve, and we give bounds for the degrees of their coordinate…
To a complex polynomial function $f$ with arbitrary singularities we associate the number of Morse points in a general linear Morsification $f_{t} := f - t\ell$. We produce computable algebraic formulas in terms of invariants of $f$ for the…