Related papers: A note on a recent attempt to prove Sendov's conje…

We give a brief proof of a recent result of Avron, Seiler and Simon.

We prove a conjecture on Rubin-Stark elements, which was recently proposed by the author, and also by Mazur and Rubin, in a special case.

The Product Conjecture for the homological Bieri-Neumann-Strebel-Renz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schuetz has recently shown that the…

The said paper [Su2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is false.

In 1966, Hedetniemi conjectured that for any positive integer $n$ and graphs $G$ and $H$, if neither $G$ nor $H$ is $n$-colourable, then $G \times H$ is not $n$-colourable. This conjecture has received significant attention over the past…

Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The…

In this paper, we give a simple counter example to the famous Hodge conjecture.

In this article we formulate a version of the analytic Novikov conjecture for semigroups rather than groups, and show that the descent argument from coarse geometry generalises effectively to this new situation.

The revised version of the claim by Hurley, Hurley and Hurley to have proved the circulant Hadamard matrix conjecture is mistaken.

The experimental findings reported in our original paper [1] (arXiv:1211.2913) have been criticized in ref.[2] (arXiv:1606.00710). We believe that the arguments brought in ref. [2] are not correct and we show evidence for this.

We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type…

Define $S(n,\beta)$ to be the set of complex polynomials of degree $n \ge 2$ with all roots in the unit disk and at least one root at $\beta$. For a polynomial $P$, define $|P|_\beta$ to be the distance between $\beta$ and the closest root…

The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…

We prove here some supplementary statements that appeared without proof in I. Panin, A. Stavrova, N. Vavilov, On Grothendieck--Serre's conjecture concerning principal $G$-bundles over reductive group schemes:I, arXiv:0905.1418

This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.

In this paper we prove the validity of a formula for computing the Alexander invariant which was originally conjectured by Bar-Natan and Dancso in [BND].

This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…

The slope conjecture proposed by Garoufalidis asserts that the Jones slopes given by the sequence of degrees of the colored Jones polynomials are boundary slopes. We verify the slope conjecture for graph knots, i.e. knots whose Gromov…