Related papers: On two Kuznetsov's conjectures

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

We provide new sufficient conditions under which Ryser's conjecture holds.

We disprove a conjecture of Kuznetsov--Shinder, which posits that $D$-equivalent simply connected varieties are $L$-equivalent, by constructing a counterexample using moduli spaces of sheaves on K3 surfaces.

In this paper we use computational methods to disprove a conjecture by Alaoglu and Erd\H{o}s regarding the superabundant numbers.

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

Two conjectures recently proposed by one of the authors are disproved

We prove several extensions of the Erdos-Fuchs theorem.

In this paper, we prove a conjecture of Schnell in the surface case.

We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)

We prove Union-Closed sets conjecture.

New cases of the multiplicity conjecture are considered.

We obtain some results related to Romanoff's theorem.

A counterexample is given for the Knaster-like conjecture of Makeev for functions on $S^2$. Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a smooth simple closed curve, are solved positively.

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

This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).

In this paper we give a counterexample to the conjecture: Let $S\in{\rm SInn}$. Then $z\cdot S$ is onto $U$.

A conjecture of Woods from 1972 is disproved.

We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The simple counterexample is adaptable to a large class of…

Nous refutons, sous une certaine hypothese combinatoire, la "nonrevisiting path conjecture". Abstract: In this article, we give, under some hypothesis, a couterexample to the nonrevisiting path conjecture.

We provide a counterexample to the Lagrangian Poincar\'e recurrence conjecture of Ginzburg and Viterbo in all dimensions $6$ and greater.