Related papers: High-low analysis and small cap decoupling over no…

In this paper we deal with analytic nonautonomous vector fields with a periodic time-dependancy, that we study near an equilibrium point. In a first part, we assume that the linearized system is split in two invariant subspaces E0 and E1.…

We construct a theory of real scalar fields that interpolates between two different theories: a Lee-Wick theory with $N$ propagator poles, including $N-1$ Lee-Wick partners, and a nonlocal infinite-derivative theory with kinetic terms…

Let S be a smooth real surface in C^2 and let p\in S be a point at which the tangent plane is a complex line. How does one determine whether or not S is locally polynomially convex at such a p --- i.e. at a CR singularity ? Even when the…

To each multiple point $p$ in a line arrangement $ \mathcal A$ in the complex projective plane we associate a local derivation $\tilde D_p \in D_0( \mathcal A)$. We show first that these derivations span the graded module of derivations…

We study the nonlocal regularization for the non-abelian gauge theories for an arbitrary value of the gauge parameter (\xi). We show that the procedure for the nonlocalization of field theories established earlier by the original authors,…

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the…

The Alexander-Hirschowitz theorem says that a general collection of $k$ double points in ${\bf P}^n$ imposes independent conditions on homogeneous polynomials of degree $d$ with a well known list of exceptions. We generalize this theorem to…

Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued…

By [arXiv:1604.00528], a list of possible holonomy algebras for pseudo-Riemannian manifolds with an indecomposable torsion free ${\rm G}_{2}^*$-structure is known. Here indecomposability means that the standard representation of the algebra…

The paper deals with a complex polynomial $H$ in two variables having - a generic highest homogeneous part (without multiple zero lines), - nonconstant lower terms. In particular, under these conditions the polynomial $H$ has at least two…

Let $p>2$ be a prime number, and $L$ be a finite extension of $\mathbb{Q}_p$, we prove Breuil's locally analytic socle conjecture for $\mathrm{GL}_2(L)$, showing the existence of all the companion points on the definite (patched)…

Assuming the Generalised Riemann Hypothesis (GRH), we show that for all k, there exist polynomials with coefficients in $\MA$ having no arithmetic circuits of size O(n^k) over the complex field (allowing any complex constant). We also build…

The criterion for an affine primary algebra over the field to be integral, is proven. Using this criterion we give a simple proof that Hilbert scheme of 0-dimensional subschemes of length $l$ of nonsingular $d$-dimensional algebraic variety…

We study the $L^2$--cohomology of certain local systems on non-compact arithmetic ball quotients $X=\Gamma \backslash \B_n$, in particular vanishing and non--vanishing results. We also give generalizations to higher dimensional ball…

Given a finite-dimensional complex simple $\omega$-Lie algebras $\mathfrak{}$ over $\mathbb{C}$. We prove that every local ,$2-$local derivation is a derivation and every local (resp. 2-local) automorphisms are automorphisms or an…

The aim of this paper is to provide the first application of Theorem 3 of [2] in a case where the dependence of the underlying equation from the real parameter is not of affine type.

In this article, we will prove that the formal degree conjecture is compatible with the Deligne-Kazhdan correspondence for quasi-split groups, assuming that the local Langlands correspondence is compatible with the Deligne-Kazhdan…

This paper generalizes the concepts of 2-local derivations and biderivations (without the skewsymmetric condition) of a finite-dimensional Lie algebra from the adjoint module to any finite-dimensional module, and determines all 2-local…

If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the…

The Recognition Theorem for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic p > 3. The main goal of this monograph is to…