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In this paper we present an infinite family of (h-)separable cowreaths with increasing dimension. Menini and Torrecillas proved in [20] that for $A=Cl(\alpha,\beta, \gamma)$, a four-dimensional Clifford algebra, and $H=H_4$, Sweedler's Hopf…

Consider an abelian variety $A$ defined over a global field $K$ and let $L/K$ be a $\Z_p^d$-extension, unramified outside a finite set of places of $K$, with $\Gal(L/K)=\Gamma$. Let $\Lambda(\Gamma):=\Z_p[[\Gamma]]$ denote the Iwasawa…

The anomalous dimensions of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) respect holomorphy to a large extent. The holomorphy conditions are reminiscent of supersymmetry, even though the SMEFT is not a…

Recently George Bergman proved that the symmetric group of an infinite set possesses the following property which we call by the {\it universality of finite width}: given any generating set $X$ of the symmetric group of an infinite set…

Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(k) of elements of the semigroup contained in the sphere of…

Let $\Gamma$ be the Fuchsian group of the first kind. For an even integer $m\ge 4$, we describe the space $H^{m/2}\left(\mathfrak R_\Gamma\right)$ of $m/2$--holomorphic differentials in terms of a subspace $S_m^H(\Gamma)$ of the space of…

In 2011, Guralnick and Tiep proved that if $G$ was a Chevalley group with Borel subgroup $B$ and $V$ an irreducible $G$-module in cross characteristic with $V^B = 0$, then the the dimension of $H^1(G,V)$ is determined by the structure of…

We study the large scale geometry of the upper triangular subgroup of PSL(2,Z[1/n]), which arises naturally in a geometric context. We prove a quasi-isometry classification theorem and show that these groups are quasi-isometrically rigid…

For classical Lie superalgebras of type I, we provide necessary and sufficient conditions for a Verma supermodule $\Delta(\lambda)$ to be such that every non-zero homomorphism from another Verma supermodule to $\Delta(\lambda)$ is…

Non-perturbative renormalization group approach suggests that a large class of nonlinear sigma models are renormalizable in three dimensional space-time, while they are non-renormalizable in perturbation theory. ${\cal N}=2$ supersymmetric…

We study a particular class of representations from the fundamental groups of punctured spheres $\Sigma_{0,n}$ to the group $\text{PSL} (2,\mathbb R)$ (and their moduli spaces), that we call \emph{super-maximal}. Super-maximal…

In this paper, we consider the limit $ \lim_{n \to \infty} \sum_{v\in S} \lambda_{Y,v}(f^{n}(x))/h_{H}(f^{n}(x)) $ where $f \colon X \longrightarrow X$ is a surjective self-morphism on a smooth projective variety $X$ over a number field,…

This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…

The main result of this paper is an application of the topology of the space $Q(X)$ to obtain results for the cohomology of the symmetric group on $d$ letters, $\Sigma_d$, with `twisted' coefficients in various choices of Young modules and…

We prove a degree-one saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on $\mathrm{SL}_2$ over any number field that is not totally real. In particular, we establish a sharp…

Given a Coxeter system $(W,S)$ and a positive real multiparameter $\bq$, we study the "weighted $L^2$-cohomology groups," of a certain simplicial complex $\Sigma$ associated to $(W,S)$. These cohomology groups are Hilbert spaces, as well as…

The Springer modules have a combinatorial property called ``coincidence of dimensions,'' i.e., the Springer modules are naturally decomposed into submodules with common dimensions. Morita and Nakajima proved the property by giving modules…

We prove that for any euclidean ring R and n at least 6, Gamma=SL_n(R) has no unbounded quasi-homomorphisms. From Bavard's duality theorem, this means that the stable commutator length vanishes on Gamma. The result is particularly…

In previous work, the authors established various bounds for the dimensions of degree $n$ cohomology and $\Ext$-groups, for irreducible modules of semisimple algebraic groups $G$ (in positive characteristic $p$) and (Lusztig) quantum groups…

We study boundary representations of hyperbolic groups $\Gamma$ on the (compactly embedded) function space $W^{\log,2}(\partial\Gamma)\subset L^2(\partial\Gamma)$, the domain of the logarithmic Laplacian on $\partial\Gamma$. We show that…