Related papers: Eigencone, saturation and Horn problems for symple…

We propose a simple one sided Monte-Carlo algorithm to distinguish, to any given degree of certainty, between certain symplectic and orthogonal groups over fields of odd order. The algorithm does not use an order oracle and works in…

For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an…

In this paper we study the rate of convergence of the eigenvalues of 1-dimensional rapidly oscillating $p-$laplacian type problems and find explicit order of convergence both in $k$ and in $\ve$. Moreover, explicit bounds on the constant…

We consider the problem of computing homogeneous coordinates of points in a zero-dimensional subscheme of a compact, complex toric variety $X$. Our starting point is a homogeneous ideal $I$ in the Cox ring of $X$, which in practice might…

We study topological groups of monotonic autohomeomorphisms on a generalized ordered space $L$. We find a condition that is necessary and sufficient for the set of all monotonic autohomeomorphisms on $L$ along with the function composition…

The saturation theorem of [Knutson-Tao '99] concerns the nonvanishing of Littlewood-Richardson coefficients. In combination with work of [Klyachko '98], it implies [Horn '62]'s conjecture about eigenvalues of sums of Hermitian matrices.…

We discuss some finite homogeneous structures, addressing the question of universality of their automorphism groups. We also study the existence of so-called Kat\v{e}tov functors in finite categories of embeddings or homomorphisms.

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle of a compact orientable manifold M. The first result is a new uniform estimate for the solutions of the Floer equation,…

In this paper, we construct a quantization functor, associating a complex vector space H(V) to a finite dimensional symplectic vector space V over a finite field of odd characteristic. As a result, we obtain a canonical model for the Weil…

We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…

Making use of theory of differentiable stacks, we study symplectic vortex equations over a compact orbifold Riemann surface. We discuss the category of representable morphisms from a compact orbifold Riemann surface to a quotient stack.…

We study two inexact methods for solutions of random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric matrix operator, the methods solve for eigenvalues and…

The class of differential-equation eigenvalue problems $-y''(x)+x^{2N+2}y(x)=x^N Ey(x)$ ($N=-1,0,1,2,3,...$) on the interval $-\infty<x<\infty$ can be solved in closed form for all the eigenvalues $E$ and the corresponding eigenfunctions…

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

This is a survey. The main subject of this survey is the homotopical or homological nature of certain structures which appear in classical problems about groups, Lie rings and group rings. It is well known that the (generalized) dimension…

We consider problems involving rich homotheties in a set S of n points in the plane (that is, homotheties that map many points of S to other points of S). By reducing these problems to incidence problems involving points and lines in R^3,…

We introduce a class of "Lipschitz horizontal" vector fields in homogeneous groups, for which we show equivalent descriptions, e.g. in terms of suitable derivations. We then investigate the associated Cauchy problem, providing a uniqueness…

We construct deformations of the small quantum cohomology rings of homogeneous spaces G/P, and obtain an irredundant set of inequalities determining the multiplicative eigenvalue problem for the compact form K of G.

We derive explicit isomorphisms between certain congruence subgroups of the Siegel modular group, the Hermitian modular group over an arbitrary imaginary-quadratic number field and the modular group over the Hurwitz quaternions of degree 2…

A square complex matrix $A$ is called (skew) $J$-Hamiltonian if $AJ$ is (skew) hermitian where $J$ is a real normal matrix such that $J^2=-I$, where $I$ is the identity matrix. In this paper, we solve the Procrustes problem to find normal…