Related papers: Zariski density and computing with $S$-integral gr…

Let $K=k(C)$ be the function field of a curve over a field $k$ and let $X$ be a smooth, projective, separably rationally connected $K$-variety with $X(K)\neq\emptyset$. Under the assumption that $X$ admits a smooth projective model $\pi:…

In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $\Gamma$, where $\Gamma \subseteq SL_{2}({\mathbb{Z}})$ is an arbitrary congruence subgroup. We…

In this work, we use the recently introduced double-dilation construction by Zwart and Coecke to construct a new categorical probabilistic theory of density hypercubes. By considering multi-slit experiments, we show that the theory displays…

In this article, we will study prime spectrum of Krasner hyperrings and Zariski topology on them, which play an important role in algebraic geometry. Then some results about the relationship between the topological properties of Spec(R) and…

Let $\Gamma < G := \operatorname{SO}(d+1, 1)$ for $d \geq 1$ be a Zariski dense, geometrically finite, discrete subgroup with critical exponent strictly greater than $d/2$. We show that $L^2(\Gamma\backslash G)$ admits a strong spectral…

We discuss recent quantitative results in connexion with Kronecker's theorem on the density of subgroups in R^n and with Dani and Raghavan's theorem on the density of orbits in the spaces of frames. We also propose several related problems.…

The Lagrangian density of an $r$-uniform hypergraph $F$ is $r!$ multiplying the supremum of the Lagrangians of all $F$-free $r$-uniform hypergraphs. For an $r$-graph $H$ with $t$ vertices, it is clear that $\pi_{\lambda}(H)\ge…

We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly…

We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…

We show that real semi-simple Lie groups of higher rank contain (infinitely generated) discrete subgroups with full limit sets in the corresponding Furstenberg boundaries. Additionally, we provide criteria under which discrete subgroups of…

Suppose $X$ is a smooth quasiprojective variety over $\cc$ and $\rho : \pi _1(X,x) \to SL(2,\cc)$ is a Zariski-dense representation with quasiunipotent monodromy at infinity. Then $\rho$ factors through a map $X\to Y$ with $Y$ either a…

We classify all locally finite joinings of a horospherical subgroup action on \Gamma \ G when \Gamma is a Zariski dense geometrically finite subgroup of G=PSL_2(R) or PSL_2(C). This generalizes Ratner's 1983 joining theorem for the case…

Let S be a fixed finite symmetric subset of SL_d(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi_q(G) with respect to the generating set pi_q(S) form a family of expanders, where pi_q is the…

A subgroup $A$ of a finite group $G$ is said to be a $CAP$-subgroup of $G$, if for any chief factor $H/K$ of $G$, either $A H= AK$ or $A\cap H = A \cap K$. Let $p$ be a prime, $S$ be a $p$-group and $\mathcal{F}$ be a saturated fusion…

We study the minimal unitary representations of non-compact groups and supergroups obtained by quantization of their geometric realizations as quasi-conformal groups and supergroups. The quasi-conformal groups G leave generalized…

We give conditions under which the monodromy group of an $A$-hypergeometric system is invariant under modifications of the collection of characters $A$. The key ingredient is a Zariski--Lefschetz type theorem for principal $A$-determinants.

We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among others the depth of their maximal subgroups. We apply these results to determine the ordinary depth of these subgroups.

We use buildings and group extensions to compute lower bounds on the top Betti numbers for the cohomology of the level p congruence subgroups of SL(3,Z) and Sp(4,Z).

For the universal family of cyclic covers of projective spaces branched along hyperplane arrangements in general position, we consider its monodromy group acting on an eigen linear subspace of the middle cohomology of the fiber. We prove…

Spectral density of quantum Ising model in two fields for large but finite number of spins $N$, is discussed in detail. When all coupling constants are of the same order, spectral densities in the bulk are well approximated by a Gaussian…