Related papers: Borel Conjecture and Dual Borel Conjecture

The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

In this paper we consider the remaining cases of Hebey-Vaugon conjecture.

We survey recent developments on the Restriction conjecture.

We show that the bunkbed conjecture remains true when gluing along a vertex. As immediate corollaries, we obtain that the bunkbed conjecture is true for forests and that a minimal counterexample to the bunkbed conjecture is 2-connected.

New cases of the multiplicity conjecture are considered.

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

In this article, we give two different proofs of why the Collatz Conjecture is false.

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

The purpose of this note is to show by constructing counterexamples that two conjectures of M\'{o}ri and Sz\'{e}kely for the Borel-Cantelli lemma are false.

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.

We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.

We prove the equivalence of Kantor's Conjecture and the Sticky Matroid Conjecture due to Poljak und Turz\'ik.

We present a question which implies a complete positive answer for the Bass-Quillen Conjecture.

The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.