Mathematics

In the generality of a rigidly-compactly generated tensor triangulated category, we introduce semi-Bousfield classes in terms of the vanishing of the tensor product in positive degrees with respect to a fixed reasonable $t$-structure. We…

We show that every stable UCT Kirchberg algebra has a principal \'etale groupoid model, and thus contains a C$^*$-diagonal. Every unital UCT Kirchberg algebra $A$ for which $[1_A]_0$ has infinite order in $K_0(A)$ is also covered by our…

Let $\mathcal{H}(b)$ be the de Branges-Rovnyak space associated to a non-extreme point $b$ of the unit ball of $H^\infty$, and let $\phi=b/a$, where $a$ is the Pythagorean mate of $b$. It is known that, if $f$ is a function holomorphic on a…

In this paper, we answer negatively to a question posed in the context of the 2025 Oberwolfach Mini-Workshop ``The Yang-Baxter Equation and Representations of Braid Groups'' regarding the existence of split extensions classifiers in the…

We consider a smooth compact manifold with boundary, $M$, embedded in a smooth manifold of the same dimension on which an amenable group $\Gamma$ acts by isometries. We do not assume $M$ to be invariant under $\Gamma$. This results in a…

We give a simple example of a polynomial contraction automorphism of $\mathbb C^d$, $ d\ge 3 $, with unbounded degree growth. Combined with Poincar\'e-Dulac theorem it provides an algebraic automorphism of $\mathbb C^d$, $ d\ge 3 $, which…

In this paper, we investigate two subclasses of analytic and univalent functions associated with the exponential mapping $\varphi(z)=e^{\alpha z},\qquad 0<\alpha\le1,$ defined via the subordination conditions $\frac{zf'(z)}{f(z)}\prec…

In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. We establish sharp multiplier estimates…

We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality…

This article is a generalization of a result in Quillen's note ``Module theory over non-unital rings'' giving a one-to-one correspondence between bilocalization of abelian categories of modules and idempotent ideals of the base ring.…

We investigate some genuine Poisson geometric objects in the modular theory of an arbitrary von Neumann algebra $\mathfrak{M}$. Specifically, for any standard form realization $(\mathfrak{M},\mathcal{H},J,\mathcal{P})$, we find a canonical…

Dobbs proved that the second iterate of almost every line in the complex plane under the exponential function is dense in the plane. In this paper, we prove an analogous result for the second iterate of the Zorich map in $\mathbb{R}^3$.

In Grayson's combinatorial description of higher K-groups, the generators are bounded acyclic binary multi-complexes of arbitrary size. Generalising work by Kasprowski, Winges and the author, we show in this paper that multi-complexes of…

In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.

We introduce the notion of $k$-regular factorizations for contractions into $k$ factors, generalizing the classical notion of regular factorization due to Sz.-Nagy and Foia\c{s}, and develop a systematic framework for their analysis. Using…

K. S. S. Nambooripad introduced an interesting class of categories known as normal categories, which are categories with subobjects, morphisms admitting factorization and having sufficiently many cones. These normal categories plays…

Let $\mathcal{H}(\mathbb{D})$ denote the space of analytic functions in the unit disc $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$. For $0<p<\infty$ and $f\in\mathcal{H}(\mathbb{D})$, let $M_p^p(r,f)=\int_0^{2\pi}|f(re^{i\theta})|^p…

We develop an ind-Banach framework for revisiting analytification in complex geometry, inspired by Bambozzi-Chiarellotto-Vanni's work on tempered cohomology. We define several ind-Banach rings of overconvergent and holomorphic power series…

Let $G$ be a finitely generated virtually abelian group and $[\sigma]\in H^2(G;\mathbb{T})$ such that $\sigma(x,y)$ is always a root of unity. We show that the nuclear dimension of the twisted group $C^*$-algebra $C^*(G,\sigma)$ is equal to…

We prove that the set of integrable functions on the unit circle for which the analogue of Paley's theorem for $H^1$ fails is residual in $L^1(\mathbb T)$. Moreover, we establish algebraic genericity and spaceability results in several…