Related papers: Borel Conjecture and Dual Borel Conjecture

We prove two conjectures on correlation inequalities for functions that are linear combinations of unimodal Boolean monotone nondecreasing functions

In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…

In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

There is a fascinating interplay and overlap between recursion theory and descriptive set theory. A particularly beautiful source of such interaction has been Martin's conjecture on Turing invariant functions. This longstanding open problem…

The paper presents a counterexample to the Hodge conjecture.

Fuglede's conjecture in $\mathbb{Q}_p$ is proved. That is to say, a Borel set of positive and finite Haar measure in $\mathbb{Q}_p$ is a spectral set if and only if it tiles $\mathbb{Q}_p$ by translation.

Despite the failure of the integral Hodge conjecture, we show that the rational Hodge conjecture implies an integral version (modulo torsion) of the absolute Hodge conjecture.

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.

A proof of Sendov's conjecture is given.

We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We prove that if a sufficiently regular even log-concave measure satisfies a certain stronger form of the dimensional Brunn-Minkowski conjecture, then it also satisfies the (B)-conjecture. Furthermore, we show that hereditarily convex…

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply…

In the present note a generalization of Borel-Cantelli Lemma is proposed.

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].

We settle in the affirmative the Graham-Sloane conjecture.

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

We give a proof of the Howe duality conjecture for the (almost) equal rank dual pairs in full generality. For arbitrary dual pairs, we prove the irreducibility of the (small) theta lifts for all tempered representations. Our proof works for…