Related papers: A note on algebraic potentials and Morales-Ramis t…
Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…
A relationship between two old mathematical subjects is observed: the theory of hypergeometric functions and the separability in classical mechanics. Separable potential perturbations of the integrable billiard systems and the Jacobi…
We prove a non-minimal modularity lifting theorem for ordinary Galois representations over imaginary quadratic fields, conditional on a local-global compatibility conjecture for ordinary torsion classes.
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…
For a class of nonassociative metagroup algebras their separability is investigated. For this purpose the cohomology theory on them is utilized. Conditions are found under which nonassociative metagroup algebras are separable. Algebras…
It is believed that any p-adic Galois representation which is potentially semistable arises from a modular form. The main theorem of Wiles establishes this modularity when the representation in question satisfies various technical…
The algebra of volume-preserving vector fields is considered. The potentials for that fields are introduced, and induced algebra of potentials is considered. It is shown, that this algebra fails to satisfy the Jacoby identity. Analogy with…
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…
In this paper the problem of classification of integrable natural Hamiltonian systems with $n$ degrees of freedom given by a Hamilton function which is the sum of the standard kinetic energy and a homogeneous polynomial potential $V$ of…
A realistic analysis shows that constraining a quantomechanical system produces the effective dynamics to be coupled with {\sl abelian/non-abelian gauge fields} and {\sl quantum potentials} induced by the {\sl intrinsic} and {\sl extrinsic…
By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of non-uniruled polarized varieties.
Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant and apply it to deduce a result on totally positive…
In this paper, the geometric approach to the virial theorem developed in \cite{CFR12} is written in terms of quasi-velocities (see \cite{CNCS07}). A generalization of the virial theorem for mechanical systems on Lie algebroids is also…
We consider several ways of decomposing models into parts of bounded size forming a congruence over a base, and show that admitting any such decomposition is equivalent to mutual algebraicity at the level of theories. We also show that a…
Experimental evidene of the last decades has made the status of "collapses of the wave function" even more shaky than it already was on conceptual grounds: interference effects turn out to be detectable even when collapses are typically…
In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics and the rigidity theory of bar-and-joint frameworks. In each…
In this paper, we study various properties of matroidal ideals.
We produce examples of complex algebraic surfaces with isolated singularities such that these singularities are not metrically conic, i.e. the germs of the surfaces near singular points are not bi-Lipschitz equivalent, with respect to the…