相关论文: Ma\~n\'e's conjectures in codimension one

In 1987, Mazur and Tate stated conjectures which, in some cases, resemble the classical Birch-Swinnerton-Dyer conjecture and its $p$-adic analog. We study experimentally three conjectures stated by Mazur and Tate using SageMath. Our…

We prove the Batyrev-Manin conjecture for smooth equivariant compactifications of forms of $\mathbb{G}_a^n$ over a global function field $F$, assuming some conditions on the boundary divisor. To verify that the leading constant agrees with…

Based on Casas-Alvero conjecture \textit{[J. Algebra, 2001]} we formulate the following conjecture.\\ \textbf{C*-algebraic Casas-Alvero Conjecture : Let $\mathcal{A}$ be a commutative C*-algebra, $n\in \mathbb{N}$ and let $P(z) =…

We prove a conjecture due to Nicolas Chevallier concerning unimodular matrices related to simultaneous Diophantine approximation to real numbers.

Based on a recent result of Mathas and the author, we prove that Uno's conjecture on representation types of Hecke algebras is true for all Hecke algebras of classical type.

Let $S\subseteq \mathbb{N}$ be a numerical semigroup with multiplicity $m$, embedding dimension $\nu$ and conductor $c=f+1=qm-\rho$ for some $q,\rho\in\mathbb{N}$ with $\rho<m$. Let Ap$(S,m) = \{w\_0<w_1 < \ldots < w_{m-1}\}$ be the Ap\'ery…

There are errors in the proof of the uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further…

The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.

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 prove the (generalized) coherence conjecture of Pappas and Rapoport. As a corollary, one theorem of Pappas an Rapoport, which describes the geometry of the special fibers of the local models for ramified unitary groups, holds…

We use the compression theorem (arxiv:math.GT/9712235) cf section 7, to prove results for equivariant configuration spaces analogous to the well-known non-equivariant results of May, Milgram and Segal.

We consider uniformly (DC) or periodically (AC) driven generalized infinite elastic chains (a generalized Frenkel-Kontorova model) with gradient dynamics. We first show that the union of supports of all the invariant measures, denoted by A,…

We settle the Hadwiger-Boltyanski Illumination Conjecture for all 1-unconditional convex bodies in ${\mathbb R}^3$ and in ${\mathbb R}^4$. Moreover, we settle the conjecture for those higher-dimensional 1-unconditional convex bodies which…

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

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…

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular, simple self-contained proofs of their two key statements.…

We prove that the Kakeya maximal conjecture is equivalent to the $\Omega$-Kakeya maximal conjecture. This completes a recent result in [2] where Keleti and Math{\'e} proved that the Kakeya conjecture is equivalent to the $\Omega$-Kakeya…

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

We prove that for two-component maps in dimension two, rank-one convexity is equivalent to quasiconvexity. The essential tool for the proof is a fixed-point argument for a suitable set-valued map going from one component to the other that…

A strong form of the Manin-Peyre conjecture with a power saving error term is proved for a certain cubic fourfold.