This paper has two objectives. First, we study lattices with skew-Hermitian forms over division algebras positive involutions. For of Albert types I and II, show that such a lattice contains an “orthogonal” basis for sublattice effectively bounded index. Second, apply this result to obtain new results in the field unlikely intersections. More specifically, prove Zilber–Pink conjecture intersect...

Fix the data (p,K,E) where p is a prime number, K a number field, and E an elliptic curve over Q. Let K∞/K denote the maximal Zp-power extension of K. Recent work provides, in some instances, detailed information about p-adic completions of Mordell-Weil groups and their associated p-adic height pairings, and the p-primary Shafarevich-Tate groups and their associated Cassels pairings, over inter...

For the unitary ensembles of N × N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For example the n-point correlation function and the spacing probabilities have nice representations in terms of this kernel. For the orthogonal and symplectic ensembles...

In this article the unitary equivalence transformation of normal matrices to tridiagonal form is studied. It is well-known that any matrix is unitarily equivalent to a tridiagonal matrix. In case of a normal matrix the resulting tridiagonal inherits a strong relation between its superand subdiagonal elements. The corresponding elements of the superand subdiagonal will have the same absolute val...

The classical Airy function has been generalised by Kontsevich to a function of a matrix argument, which is an integral over the space of (skew) hermitian matrices of a unitary-invariant exponential kernel. In this paper, the Kontsevich integral is generalised to integrals over the Lie algebra of an arbitrary connected compact Lie group, using exponential kernels invariant under the group. The ...

We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspace methods. We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding precondi...

A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The theoretical spectral analysis focuses on the case of matrix sequences related to FE approximations on uniform structured meshes, by referring to spectral tools der...