Related papers: Wahl's conjecture for a minuscule G/P

The Wiegold conjecture holds for the small Ree groups for $k$-tuples where $k \geq 5$.

We prove that the Thin Sandwich Conjecture in general relativity is valid, provided that the data $(g_{ab},\dot g_{ab})$ satisfy certain geometric conditions. These conditions define an open set in the class of possible data, but are not…

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for…

We prove the Aharoni Berger Conjecture

Let $X$ denote a flag variety of type $A$ or type $C$. We construct a canonical Frobenius splitting of $X \times X$ which vanishes with maximal multiplicty along the diagonal. This way we verify a conjecture by Lakshmibai, Mehta and…

An analog of Picard's little theorem for entire functions of matrices is proved.

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

In this paper we present a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. Motivated by this conjecture, we determine all intermediate subfactors of Goodman-Harpe-Jones…

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

The Erd\"os-Hajnal conjecture states that for every graph $H$, there exists a constant $\delta(H) > 0$ such that every graph $G$ with no induced subgraph isomorphic to $H$ has either a clique or a stable set of size at least…

The Galois Alperin weight (GAW) conjecture has been reduced to the inductive GAW condition for simple groups. We proceed in two steps to refine this reduction. First, we propose the blockwise Galois Alperin weight (BGAW) conjecture and…

We prove that for every k, there exists $c_k>0$ such that every graph G on n vertices not inducing a path $P_k$ and its complement contains a clique or a stable set of size $n^{c_k}$.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We prove the Breuil-Mezard conjecture for split non-scalar residual representations of Gal(Qp/Qp) by local methods. Combined with the cases previously proved in [18] and [24], this completes the proof of the conjecture (when p>3). As a…

We give a number new examples analytically and numerically to confirm the Kohler conjecture. It turned out that for a rather large class of nonnegative functions the equality (A) hold.

We propose an Artinian version of Berger's Conjecture for curves, concerning the module of K\"ahler differentials of an algebra. Our version implies Berger's Conjecture in characteristic 0. We establish our Artinian Berger Conjecture in a…

We give a proof of the Howe duality conjecture for the (almost) equal rank dual pairs in full generality. For arbitrary dual pairs, we prove the irreducibility of the (small) theta lifts for all tempered representations. Our proof works for…

Let $1 \to N \to G \to G/N \to 1$ be a short exact sequence of countable discrete groups and let $B$ be any $G$-$C^*$-algebra. In this paper, we show that the strong Novikov conjecture with coefficients in $B$ holds for such a group $G$…

We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.