Related papers: Non-integrability Criterium for Normal Variational…

We consider the Arveson-Douglas conjecture on the essential normality of homogeneous submodules corresponding to algebraic subvarieties of the unit ball. We prove that the property of essential normality is preserved by isomorphisms between…

In the article the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables is studied. By integrability we mean the presence of reductions of a chain to a system of hyperbolic…

We study the arithmetic of division fields of semistable abelian varieties A over the rationals. The Galois group of the 2-division field of A is analyzed when the conductor is odd and squarefree. The irreducible semistable mod 2…

We produce examples of solutions to the non-abelian gravitating vortex equations, which are a dimensional reduction of the K\"aher-Yang-Mills- Higgs equations. These are equations for a K\"ahler metric and a metric on a vector bundle. We…

We compute presentations of crystalline framed deformation rings of a two dimensional representation $\bar{\rho}$ of the absolute Galois group of $\mathbb{Q}_p$, when $\bar{\rho}$ has scalar semi-simplification, the Hodge-Tate weights are…

We introduce a novel extension to robust control theory that explicitly addresses uncertainty in the value function's gradient, a form of uncertainty endemic to applications like reinforcement learning where value functions are…

We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois theory of general systems of polynomial equations, because…

A quantum thermodynamic system can conserve non-commuting observables, but the consequences of this phenomenon on relaxation are still not fully understood. We investigate this problem by leveraging an observable-dependent approach to…

We prove modularity for any irreducible crystalline $\ell$-adic odd 2-dimensional Galois representation (with finite ramification set) unramified at 3 verifying an "ordinarity at 3" easy to check condition, with Hodge-Tate weights $\{0, w…

We apply KAM theory to the equation of the forced relativistic pendulum to prove that all the solutions have bounded momentum. Subsequently, we detect the existence of quasiperiodic solutions in a generalized sense. This is achieved using a…

We establish non-unirational versions of Hilbert Irreducibility for all Hilbert modular surfaces which are of K3 type. As an application we prove new instances of the regular Inverse Galois Problem for the simple groups…

We extend the Eruguin result exposed in the paper "Construction of the whole set of ordinary differential equations with a given integral curve" published in 1952 and construct a differential system in $\Bbb{R}^N$ which admits a given set…

We seek to derive the probability--expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the…

The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean…

We study integral points on varieties with infinite \'etale fundamental groups. More precisely, for a number field $F$ and $X/F$ a smooth projective variety, we prove that for any geometrically Galois cover $\varphi\colon Y \to X$ of degree…

In this paper we present a simple, algorithmic test to establish if a Hamiltonian system is maximally superintegrable or not. This test is based on a very simple corollary of a theorem due to Nekhoroshev and on a perturbative technique…

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…

We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…

In this paper we obtain new quantitative forms of Hilbert's Irreducibility Theorem. In particular, we show that if $f(X, T_1, \ldots, T_s)$ is an irreducible polynomial with integer coefficients, having Galois group $G$ over the function…

We study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical $N$--body problem. We introduce a variational Morse--like index for a class of collision solutions and, using the…