Related papers: Borel Conjecture and Dual Borel Conjecture
In this paper we prove the conjecture posed by Kl\'en et al. in \cite{kvz}, and give optimal inequalities for generalized trigonometric and hyperbolic functions.
We prove equivalences of derived categories for the various mirrors in the Batyrev-Borisov construction. In particular, we obtain a positive answer to a conjecture of Batyrev and Nill. The proof involves passing to an associated category of…
We prove a conjecture of Meszaros and Morales on the volume of a flow polytope. Independently from our work, Zeilberger sketched a proof of their conjecture. In fact, our proof is the same as Zeilberger's proof. The purpose of this note is…
We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.
We investigate a result on convergence of double sequences of numbers and how it extends to measurable functions.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We study a natural analogue of Collatz's Conjecture for polynomials over $\mathbb{F}_2$.
In this paper, the abc conjecture is negated under certain conditions
We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…
In this paper we prove a conjecture of B. Shoikhet which claims that two quantization procedures arising from Fourier dual constructions actually coincide.
Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
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.
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
In this paper, we prove a conjecture of Schnell in the surface case.
We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
The conjectures of Manin and Peyre are confirmed for a certain threefold.
We show that a weak form of the generalized Bocherer's conjecture implies multiplicity one for Siegel cusp forms of degree 2.
The article provides a counterexample to a conjecture by Blocki-Zwonek.