Related papers: A bijectional attack on the Razumov-Stroganov conj…

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.

The Razumov-Stroganov conjecture relates the ground-state coefficients in the even-length dense O(1) loop model to the enumeration of fully-packed loop configuration on the square, with alternating boundary conditions, refined according to…

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

We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .

We survey recent developments on the Restriction conjecture.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

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.

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…

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

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

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

We study algebras on which the Berenstein-Zelevinsky conjecture is true. In particular, we prove that this conjecture is true "up to localization".

The Collatz conjecture is explored using polynomials based on a binary numeral system. It is shown that the degree of the polynomials, on average, decreases after a finite number of steps of the Collatz operation, which provides a weak…

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

A proof of Sendov's conjecture is given.

We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…

We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.

The article provides a counterexample to a conjecture by Blocki-Zwonek.