Related papers: A note on lattice coverings

The paper presents a counterexample to the Hodge conjecture.

The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches.

The purpose of this note is to attach a name to a natural class of combinatorial problems and to point out that this class includes many important special cases. We also show that a simple problem of placing nonoverlapping labels on a…

We provide simple proofs of analogues for coverings numbers of lattices of several recently studied basic statements on the ranks of tensors. We highlight the differences and analogies between the proofs in both settings.

We consider the problem of covering $\mathbb{Z}^2$ with a finite number of sublattices of finite index, satisfying a simple minimality or non-degeneracy condition. We show how this problem may be viewed as a projective (or homogeneous)…

The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.

The purpose of this note is to give counterexamples to the containment $I^{(3)}\subset I^2$ over the real numbers.

This note is the follow up to a paper by M. Waldschmidt.

Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.

This note provides a counterexample to a proposition stated in [J. Differ. Equ. 261.4 (2016) 2528--2551] regarding the neighborhood of certain $4\times 4$ symplectic matrices.

The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.

We present some illustrations for the claim that already by looking at the ground states of classical lattice models, one may meet some interesting and non-trivial structures.

Let L be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of L is nonpositive.

This is an update of my problem list.

In this paper we study the lattice point covering property of some regular polygons in dimension 2.

This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.

A conjecture regarding the structure of expander graphs is discussed.

The isometry class of the intersection form of a compact complex surface can be easily determined from complex-analytic invariants. For projective surfaces the primitive lattice is another naturally occurring lattice. The goal of this note…

This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…

These notes are connected to a "potpourri" topics class and deal with some basic issues involving norms and convexity.