Related papers: A Counter Example To the Hodge Conjecture

A very simple but useful almost sure convergence theorem of probability is given.

We present a simple dyadic construction that yields a new counterexample to Zygmund's conjecture. Our result recovers Soria's classical result in dimension three, through a different construction, and gives new ones in all other dimensions…

We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…

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

We prove Union-Closed sets conjecture.

We provide a counterexample to P.~Olver's freeness conjecture for $C^\omega$ transformations.

In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.

We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

We present a relative form of the Toponogov comparison theorem.

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

In this article we develop counterexamples to the Hasse principle using only techniques from undergraduate number theory and algebra. By keeping the technical prerequisites to a minimum, we hope to provide a path for nonspecialists to this…

The paper provides a version of the rational Hodge conjecture for $\3\dg$ categories. The noncommutative Hodge conjecture is equivalent to the version proposed in \cite{perry2020integral} for admissible subcategories. We obtain examples of…

In this paper the circulant Hadamard conjecture is proved.

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

In this short note we give counterexamples to several results related to extension theorems published recently.

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

We describe in some details an idea of M. Kontsevich how one can try to find a counterexample to the Hodge conjecture using tropical geometry.

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

We prove the Aharoni Berger Conjecture