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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A New Framework for SIMD Bootstrapping in Polynomial Modulus
多项式 模数 SIMD自举 新框架
2023/4/28
In this series of work, we aim at improving the bootstrapping paradigm for fully homomorphic encryption (FHE). Our main goal is to show that the amortized cost of bootstrapping within a polynomial mod...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On polynomial method and its application（II）
多项式方法 应用 代数
2023/5/17
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
Let K be an algebraically closed field of characteristic zero and let f ∈ K[x]. The m-th cyclic resultant of f is rm = Res(f, xm − 1). A generic monic polynomial is determined by its full sequen...
Polynomial-time Isomorphism Test for Groups with Abelian Sylow Towers
polynomial-time algorithm, group isomorphism, solvable group
2012/12/3
We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial nlog n bound on the time complexity for the general case has not been improved over the past fou...
Simple G-graded algebras and their polynomial identities
graded algebra polynomial identity
2011/9/19
Abstract: Let G be any group and F an algebraically closed field of characteristic zero. We show that any two G-graded finite dimensional G-simple algebras over F are G-graded isomorphic if and only i...
Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups
Residually nilpotent group entropy of automorphisms of groups pseudo-Anosov dilatation
2011/9/15
Abstract: We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various n...
A polynomial bound on solutions of quadratic equations in free groups
polynomial bound quadratic equations free groups Group Theory
2011/8/31
Abstract: We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutio...
Tropical varieties with polynomial weights and corner loci of piecewise polynomials
Tropical varieties polynomial weights corner loci of piecewise polynomials
2011/2/28
Counting Euler characteristics of the discriminant of the quadratic equation in terms of
Newton polytopes in two different ways, G. Gusev ([Gus]) found an unexpected relation for
mixed volumes of tw...
On Stably free modules over Laurent polynomial rings
Stably free modules Hermite rings Unimodular rows
2011/2/21
We prove constructively that for any finite-dimensional commu-tative ring R and n dim(R) + 2, the group En(R[X,X−1]) acts transitively on Umn(R[X,X−1]). In particular, we obtain that for...
On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
Differential Galois Theory Darboux theory of Integrability Poincar´ e problem,
2011/2/24
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type folia-tion.
Hyperbolicity of the invariant sets for the real polynomial maps
Cantor set Complex dynamic Hyperbolic Logistic map Polynomial map
2011/2/25
It is well known that for a > 4, the dynamical behaviors of the logistic map fa(x) = ax(1 − x) on the maximal invariant compact set are “simple”, which could be clearly explained by the theories...
Mathieu Subspaces of Univariate Polynomial Algebras
Mathieu subspaces the (Strong) Image Conjecture the (Strong) Integral Conjecture
2011/1/20
We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals.We then deduce that for some classes of classical univariate
orthogonal...
Modular absolute decomposition of equidimensional polynomial ideals
Modular absolute decomposition equidimensional polynomial ideals
2011/2/25
In this paper, we present a modular strategy which describes key properties of the absolute
primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficie...
Igusa's p-adic local zeta function associated to a polynomial mapping and a polynomial integration measure
Igusa's p-adic local zeta function associated polynomial mapping polynomial integration measure
2011/2/25
For p prime, we give an explicit formula for Igusa’s local zeta function associated to a polynomial mapping f = (f1, . . . , ft) : Qn p ! Qt p,with f1, . . . , ft 2 Zp[x1, . . . , xn], and an integrat...
Polynomial identity rings as rings of functions, II
Polynomial identity ring central simple algebra trace ring
2011/1/18
In characteristic zero, Zinovy Reichstein and the author generalized the usual relationship between irreducible Zariski closed subsets of the affine space.