Related papers: The local Gross-Prasad conjecture over $\mathbb{R}…

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

We reprove the Local Langlands Correspondence for $\GL_n$ over $p$-adic fields as well as the existence of $\ell$-adic Galois representations attached to (most) regular algebraic conjugate self-dual cuspidal automorphic representations, for…

We present a detailed analysis of the set theoretical proof of Wigner for Bell type inequalities with the following result. Wigner introduced a crucial assumption that is not related to Einstein's local realism, but instead, without…

We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…

We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect for an arbitrary extension of number fields. As an application, we prove new cases of Gross's finiteness conjecture (also known as the…

We present a proof of a multidimensional version of Peres-Schlag's theorem on Diophantine approximations with lacunary sequences.

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

We consider a class of linear eigenvalue problems depending on a small parameter epsilon in which the series expansion for the eigenvalue in powers of epsilon is divergent. We develop a new technique to determine the precise nature of this…

In this paper we give a proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudo-differential operators is equivalent to condition ($\Psi$). This condition rules out certain sign changes of the imaginary…

Prasad and Takloo-Bighash proposed a conjecture which predicts a necessary condition in terms of epsilon factors for representations of $\mathrm{GL}_n(F)$ and its inner forms to have linear periods. In this rather expository article, we…

We provide a self contained proof of a result of Dudley [Dud64]} which shows that a bounded convex-body in $\Re^d$ can be $\varepsilon$-approximated, by the intersection of $O_d\bigl(\varepsilon^{-(d-1)/2} \bigr)$ halfspaces, where $O_d$…

Let F be a non-archimedean local field, of characteristic 0. Let V be a finite dimensional vector space over F and q be a non-degenerate quadratic form on V. Denote d the dimension of V and G=SO(d) the special orthogonal group of (V,q). Let…

Fuglede's conjecture states that for a subset $\Omega$ of a locally compact abelian group $G$ with positive and finite Haar measure, there exists a subset of the dual group of $G$ which is an orthogonal basis of $L^{2}(\Omega)$ if and only…

For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy, thus generalising the well-known relative energy method. To this end, we adapt…

The local non-tempered Gan-Gross-Prasad conjecture suggests that, for a pair of irreducible Arthur type representations of two successive general linear groups, they have a non-zero Rankin-Selberg period if and only if they are "relevant".…

We give a new local proof of Breuil-M\'ezard conjecture for two dimensional representations of the absolute Galois group of $\mathbb{Q}_p$, when $p\ge 5$ and the representation has scalar endomorphisms.

Using a ramified cover of the two-sphere by the torus, we prove a local optimal inequality between the diastole and the area on the two-sphere near a singular metric. This singular metric, made of two equilateral triangles glued along their…

We prove a simple criterion of exponential tightness for sequences of Gaussian r.v.'s with values in a separable Banach space from which we deduce a general result of Large Deviations which allows easily to obtain LD estimates in various…

This is the last in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…

This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be…