Mathematics

Given a finite abelian group $G$ and a Sylow $p$-subgroup $N_p$, we prove that the $KU_G/p$-local sphere spectrum is equivalent to the homotopy fixed points of a $p$-complete $KO_{N_p}$-module spectrum. Then we compute the…

We study Lusin-measurable functions with values in locally convex spaces. In particular, the behavior of pointwise limits of sequences of Lusin-measurable functions and exhibit pathological phenomena arising in the nonmetrizable setting.…

The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…

We provide the first example of a finitely presented, and the first example of a simple, group of non-uniform exponential growth. The example is given by Thompson's group V.

Consider, on the space of marked groups, the map $\mathrm{Res}_{\mathcal{C}}$ which associates to a marked group its greatest residually-$\mathcal{C}$ quotient, for different sets $\mathcal{C}$ of groups. Except for trivial cases, this map…

We characterize all lattices $\Lambda \subset \mathbb{R}^2$ and all compactly supported functions $g \in L^2(\mathbb{R})$ for which the Gabor system $\left \{ e^{2\pi i s x} g(x-t) : (t,s) \in \Lambda \right \}$ forms an orthonormal basis…

We prove that the spaces $\ell_p(C(\alpha))$ and $\ell_p(C[0,1])$ have the uniform primary factorisation property whenever $\alpha$ is an ordinal and $1<p\leq\infty$. For the case $p=1$, we establish a general criterion ensuring that…

We show that groups with a mild form of non-positive curvature (a navigable path system) satisfy the weak rank rigidity conjecture: they either have linear divergence or a Morse element. This class includes discrete groups of projective…

In this note, we provide a family of $2\times 2$ tetrablock contractions that have tetrablock isometric dilation, but the corresponding fundamental operators do not commute. This answers a question raised by Bhattacharyya [Indiana Univ.…

The classes of abelian groups that are (uniformly) strongly Hopfian abelian groups, and dually, (uniformly) strongly co-Hopfian abelian groups have been studied by several authors, including Abdelalim (2015) and Abdelalim-Chillali-Essanouni…

This paper studies frames in Hilbert spaces generated by the orbits of (in)-finitely many vectors under a single operator, presenting new results on multiplication operators and operators composed of Jordan blocks, which generalizes…

Martingales, Markov processes and Laws of Large Numbers have been well studied in the Riesz space (vector lattice) setting. There has, however, been no attention given in the Riesz space setting to Laws of Small Numbers or to the so called…

For a conditional expectation operator $T$ on a Dedekind complete Riesz space, we give representations of the $T$-strong duals of $L^1(T)$ and $L^\infty(T)$. The representation for the $T$-strong dual of $L^1(T)$ follows from the known…

We show that the affine cactus group is a CAT$(0)$ group for all degrees. Furthermore, we show that the affine cactus group $AJ_3$ of degree three is a hyperbolic group.

Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric properties. Using recent structural results of Mili\'cevi\'c,…

Nagano spaces are compact symmetric spaces that admit large transformation groups. They include for instance all the Grassmannians and the Einstein Universes. In this paper, we study a Kobayashi-type pseudometric on domains in real-type…

Let $\Gamma_{2n}^\omega(p)$ be the level-$p$ principal congruence subgroup of $\text{Sp}_{2n}(\mathbb{Z})$ for all prime $p$. Borel--Serre demonstrated that the cohomology of $\Gamma_{2n}^\omega(p)$ vanishes above degree $n^2$. We prove…

We study free products, that is, coproducts, in the category of Banach lattices and contractive lattice homomorphisms. We give a concrete construction of the free product of an arbitrary family of Banach lattices as a quotient of a free…

We propose the systematic study of presentations that can be generalised over a continuous open group monomorphism. Presentations with this property can turn well-known presentations such as those for as orientable surface groups, Artin…

This article investigates $k$-regular factorizations of characteristic functions associated with completely non-coisometric row contractions. In this setting, a one-to-one correspondence is established between chains of joint invariant…