相关论文: Counterexamples to a conjecture of Woods
We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.
We provide a counterexample to P.~Olver's freeness conjecture for $C^\omega$ transformations.
We prove Stanley's plethysm conjecture for the $2 \times n$ case, which composed with the work of Black and List provides another proof of Foulkes conjecture for the $2 \times n$ case. We also show that the way Stanley formulated his…
In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
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 Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…
In this paper we discuss an obstruction to the integral Hodge conjecture, which arises from certain behavior of vanishing cycles. This allows us to construct new counter-examples to the integral Hodge conjecture. One typical such…
A proof of Smale's mean value conjecture from 1981 is given.
An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.
This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].
We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.
This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.
We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.
This paper is cancelled
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.
In this paper, we show that the minimal model theory does not hold in characteristic two. More precisely, we construct counter-examples to the relative abundance conjecture.
Recently Engel et al. (2025) have shown that the integral Hodge conjecture fails for very general abelian varieties. Using Deligne's theory of absolute Hodge cycles, we deduce a similar statement for the integral Tate conjecture.
In 1975 Stein conjectured that in every $n\times n$ array filled with the numbers $1, \dots, n$ with every number occuring exactly $n$ times, there is a partial transversal of size $n-1$. In this note we show that this conjecture is false…