Related papers: A density theorem for the difference Galois groups…

Let F be a finitely generated field of characteristic zero and \Gamma<GL_n(F) a finitely generated subgroup. For an element g in \Gamma, let Gal(F(g)/ F) be the Galois group of the splitting field of the characteristic polynomial of g over…

We obtain Fuchs decomposition theorem for regular singular differential modules over a large class of differential rings. We provide a definition of regularity inspired by differential Galois theory and we deduce the classical equivalence…

Using the Kuznetsov formula, we prove several density theorems for exceptional Hecke and Laplacian eigenvalues of Maass cusp forms of weight 0 or 1 for the congruence subgroups $\Gamma_0(q)$, $\Gamma_1(q)$, and $\Gamma(q)$. These improve…

In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…

Let k be a differential field and C its subfield of constants. In general a differential extension K of k add some new constants to C, and it is difficult to prove that C stay unchangeable under the extension K; This situation is provided…

The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal…

We prove a function-field version of Chebotarev's density theorem in the framework of difference algebraic geometry by developing the notion of Galois coverings of generalised difference schemes, and using Hrushovski's twisted Lang-Weil…

We explore the dependence of the minimal integral Mahler measure of Galois quartic fields on the discriminant of the field. We obtain density results which are conditional on the ABC conjecture as well as several unconditional results.

We introduce the parameterized generic Galois group of a q-difference module, that is a differential group in the sense of Kolchin. It is associated to the smallest differential tannakian category generated by the q-difference module,…

We develop algorithms to compute the differential Galois group corresponding to a one-parameter family of second order homogeneous ordinary linear differential equations with rational function coefficients. More precisely, we consider…

The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new homotopy double groupoid of a map of spaces, which includes…

One of the key points in Galois theory via field extensions is to build up a correspondence between subfields of a field and subgroups of its automorphism group, so as to study fields via methods of groups. As an analogue of the Galois…

We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between…

We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the…

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields, and the…

We explore systems of polynomial equations where we seek complex solutions with absolute value 1. Geometrically, this amounts to understanding intersections of algebraic varieties with tori -- Cartesian powers of the unit circle. We study…

We prove in a large number of cases, that a Zariski dense discrete subgroup of a simple real algebraic group $G$ which contains a higher rank lattice is a lattice in the group $G$. For example, we show that a Zariski dense subgroup of…

We give conditions under which the monodromy group of an $A$-hypergeometric system is invariant under modifications of the collection of characters $A$. The key ingredient is a Zariski--Lefschetz type theorem for principal $A$-determinants.

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

This paper is dedicated to the differential Galois theory in the complex analytic context for Lie-Vessiot systems. Those are the natural generaliza- tion of linear systems, and the more general class of differential equations adimitting…