Related papers: Weak coherence of groups and finite decomposition …

We introduce the notion of weak commensurabilty of arithmetic subgroups and relate it to the length equivalence and isospectrality of locally symmetric spaces. We prove many strong consequences of weak commensurabilty and derive from these…

When one studies the structure (e.g. graded ideals, graded subspaces, radicals, ...) or graded polynomial identities of graded algebras, the grading group itself does not play an important role, but can be replaced by any other group that…

In recent literature, it has been argued that a mild form of the Weak Gravity Conjecture (WGC) is satisfied by wide classes of effective field theories in which higher-derivative corrections can be shown to shift the charge-to-mass ratios…

Condensed mathematics as developed by Clausen and Scholze yields a version of derived functors over the category of continuous $G$-modules for a Hausdorff topological group $G$. We study the resulting notion of group cohomology and its…

Let $G$ be an almost simple, simply connected algebraic group defined over a number field $k$, and let $S$ be a finite set of places of $k$ including all infinite places. Let $X$ be the product over $v\in S$ of the symmetric spaces…

We introduce a class of complex manifolds which we call weakly holomorphic homogeneous regular manifolds (wHHR) manifolds. As the name suggests, this class contains the so-called holomorphic homogeneous regular manifolds but also other…

A notion of evolutionary $\Gamma$-convergence of weak type is introduced for sequences of operators acting on time-dependent functions. This extends the classical definition of $\Gamma$-convergence of functionals due to De Giorgi. The…

The central aim of this monograph is to provide decomposition results for quasi-coherent sheaves on the moduli stack of one-dimensional formal groups. These results will be based on the geometry of the stack itself, particularly the height…

This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various `nonpositive…

Equationally compact subgroups of countable groups were introduced by Banaschewski. For all known cases the orbit closure of such a subgroup is a countable subset in the space of subgroups and has finite Cantor-Bendixson rank. We show 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…

We analyse the structure of the quotient $\mathrm{A}_\sim(\Gamma,X,\mu)$ of the space of measure-preserving actions of a countable discrete group by the relation of weak equivalence. This space carries a natural operation of convex…

The purpose of this work is to develop a version of Forman's discrete Morse theory for simplicial complexes, based on internal strong collapses. Classical discrete Morse theory can be viewed as a generalization of Whitehead's collapses,…

The concept of (stable) weak containment for measure-preserving actions of a countable group $\Gamma$ is analogous to the classical notion of (stable) weak containment of unitary representations. If $\Gamma$ is amenable then the Rokhlin…

We show that the image of repeated differentiation on weak cusp forms is precisely the subspace which is orthogonal to the space of weakly holomorphic modular forms. This gives a new interpretation of the weakly holomorphic Hecke…

A compact space is said to be weakly Radon-Nikod\'ym if it is homeomorphic to a weak*-compact subset of the dual of a Banach space not containing an isomorphic copy of $\ell_1$. In this work we provide an example of a continuous image of a…

Deformation K-theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2-periodic above the rational cohomological dimension of G…

Let $\Gamma$ be a discrete group. A $C^*$-algebra $A$ is an exotic $C^*$-algebra (associated to $\Gamma$) if there exist proper surjective $C^*$-quotients $C^*(\Gamma)\to A\to C^*_r(\Gamma)$. In this paper, we show that a large class of…

We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called {\em pseudoharmonic morphisms}, include harmonic morphisms…

Graphons are analytic objects representing limits of convergent sequences of graphs. Lov\'asz and Szegedy conjectured that every finitely forcible graphon, i.e. any graphon determined by finitely many graph densities, has a simple…