Related papers: The matrix $A_2$ conjecture fails, i.e. $3/2>1$

It has been conjectured that the two-dimensional N=2 Wess-Zumino model with a quasi-homogeneous superpotential provides the Landau-Ginzburg description of the N=2 superconformal minimal models. For the cubic superpotential W=(lambda)…

The abelian and monoidal structure of the category of smooth weight modules over a non-integrable affine vertex algebra of rank greater than one is an interesting, difficult and essentially wide open problem. Even conjectures are lacking.…

A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two $\mathbb Z/2$-spaces is equal to the minimum of their $\mathbb Z/2$-indexes. The main purpose of this article is to study the…

We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into…

We show that for an individual Riesz transform in the setting of doubling measures, the scalar $T1$ theorem fails when $p \neq 2$: for each $ p \in (1, \infty) \setminus \{2\}$, we construct a pair of doubling measures $(\sigma, \omega)$ on…

It is conjectured that the dual variety of every smooth nonlinear subvariety of dimension $> \frac{2N}{3}$ in projective $N$-space is a hypersurface, an expectation known as the duality defect conjecture. This would follow from the truth of…

For a tuple $T$ of Hilbert space operators, the 'commuting dilation constant' is the smallest number $c$ such that the operators of $T$ are a simultaneous compression of commuting normal operators of norm at most $c$. We present numerical…

Let $D\geq 3$ denote an integer. For any $x\in \mathbb F_2^D$ let $w(x)$ denote the Hamming weight of $x$. Let $X$ denote the subspace of $\mathbb F_2^D$ consisting of all $x\in \mathbb F_2^D$ with even $w(x)$. The $D$-dimensional halved…

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 study the $l^p$ norms of a class of weighted mean matrices whose diagonal terms are given by $n^{\alpha}/\sum^{n}_{i=1}i^{\alpha}$ with $\alpha > -1$. The $l^p$ norms of such matrices are known for $p \geq 2, (\alpha+1)p >1$ and $1<p…

We prove that for any 4 points in a (2-2) configuration, there is no linear dependence between the associated time-frequency translates of any $L^2(\R)$ function

Conjugations commuting with $\mathbf{M}_z$ and intertwining $\mathbf{M}_z$ and $\mathbf{M}_{\bar z}$ in $L^2(\mathcal{H})$, where $\mathcal{H}$ is a Hilbert space, are characterized. We also investigate which of them leave invariant the…

We prove the (generalized) principal pivot transform is matrix monotone, in the sense of the L\"owner ordering, under minimal hypotheses. This improves on the recent results of J. E. Pascoe and R. Tully-Doyle, Monotonicity of the principal…

We prove that the forcing axiom $MA^{1.5}_{\aleph_2}(\mbox{stratified})$ implies $\Box_{\omega_1, \omega_1}$. Using this implication, we show that the forcing axiom $MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$ is inconsistent. We also derive weak…

A matrix-valued measure $\Theta$ reduces to measures of smaller size if there exists a constant invertible matrix $M$ such that $M\Theta M^*$ is block diagonal. Equivalently, the real vector space ${\mathscr A}$ of all matrices $T$ such…

The theorem on the existence of three commuting contractions on a Hilbert space and of a linear homogeneous matrix function of three independent variables for which the generalized von Neumann inequality fails is proved.

Let $n \ge 2$, $p \in (1, \, +\infty)$ be given and let $\Sigma$ be a $n$-dimensional, closed hypersurface in $\mathbb{R}^{n+1}$. Denote by $A$ its second fundamental form, and by $\mathring{A}$ the tensor $A - \frac{1}{n} A^i_i g$ where $g…

The analogue of P\'olya's conjecture is shown to fail for the fractional Laplacian (-Delta)^{alpha/2} on an interval in 1-dimension, whenever 0 < alpha < 2. The failure is total: every eigenvalue lies below the corresponding term of the…

We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…

Let $w=(w_1, w_2)$ be a pair of positive real numbers with $w_1+w_2=1$ and $w_1\ge w_2$. We show that the set of $w$-weighted singular vectors in $\mathbb R^2$ has Hausdorff dimension $2- \frac{1}{1+w_1}$. This extends the previous work of…