Related papers: A semigroup with linearithmic Dehn function

An important subcase of the hidden subgroup problem is equivalent to the shift problem over abelian groups. An efficient solution to the latter problem would serve as a building block of quantum hidden subgroup algorithms over solvable…

We prove that $n^{7/3}$ is an isoperimetric function for a group of Stallings that is finitely presented but not of type $\mathcal{F}_3$. Note: The authors with Robert Young have now proved a quadratic Dehn function for this group. See…

We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry…

Any Lie group G acting on a Euclidean nonvoid open subset M can be seen as a subgroup of the smooth diffeomorphisms Diff^\infty(M,M) of M into itself. Thus actions by such Lie groups G correspond to smooth coordinate transforms on M which,…

In this note, we announce the first results on quasi-isometric rigidity of non-nilpotent polycyclic groups. In particular, we prove that any group quasi-isometric to the three dimenionsional solvable Lie group Sol is virtually a lattice in…

We introduce a Grothendieck group $E_n$ for bounded polytopes in $\mathbb R^n$. It differs from the usual Euclidean scissors congruence group in that lower-dimensional polytopes are not ignored. We also define an analogous group $L_n$ using…

In this paper we prove that every collection of measurable functions $f_\alpha$, $|\alpha|=m$ coincides a.e. with $m$th order derivatives of a function $g\in C^{m-1}$ whose derivatives of order $m-1$ may have any modulus of continuity…

Given a semigroup $S$ generated by its squares, we determine the complex-valued solutions of the following system of cosine-sine functional equations \begin{align*} f(xy)=f(x)g_{1}(y)+g_{1}(x)f(y)+\lambda_{1}^{2}\,h(x)h(y),\; x,y\in S,\\…

A unitary representation of a, possibly infinite dimensional, Lie group G is called semi-bounded if the corresponding operators id\pi(x) from the derived representations are uniformly bounded from above on some non-empty open subset of the…

We propose a way of associating to each finitely generated monoid or semigroup a formal language, called its loop problem. In the case of a group, the loop problem is essentially the same as the word problem in the sense of combinatorial…

An example of an extension of a completely simple semigroup U by a group H is given which cannot be embedded into the wreath product of U by H. On the other hand, every central extension of U by H is shown to be embeddable in the wreath…

We show that an arithmetic lattice $\Gamma$ in a semi-simple Lie group $G$ contains a torsion-free subgroup of index $\delta(v)$ where $v = \mu (G/\Gamma)$ is the co-volume of the lattice. We prove that $\delta$ is polynomial in general and…

For a generalized permutohedron $Q$ the enumerator $F(Q)$ of positive lattice points in interiors of maximal cones of the normal fan $\Sigma_Q$ is a quasisymmetric function. We describe this function for the class of nestohedra as a Hopf…

Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. This fact is used to find a unique semiclassical representation without the…

We consider continuous semigroups of analytic functions $\{\Phi_t\}_{t\geq0}$ in the so-called Gordon-Hedenmalm class $\mathcal{G}$, that is, the family of analytic functions $\Phi:\mathbb C_+\to \mathbb C_+$ giving rise to bounded…

Let T_t = e^{-tA} be a bounded analytic semigroup on Lp, with 1<p<\infty. It is known that if A and its adjoint A^* both satisfy square function estimates \bignorm{\bigl(\int_{0}^{\infty}| A^{1/2} T_t(x)|^2\, dt\,\bigr)^{1/2}_{Lp} \lesssim…

We construct the first examples of finitely presented groups with cubic Dehn function containing a finitely generated infinite torsion subgroup. Moreover, we show that any infinite free Burnside group with sufficiently large odd exponent…

We treat two related trigonometric functional equations on semigroups. First we solve the $\mu$-sine subtraction law \[\mu(y) k(x \sigma(y))=k(x) l(y)-k(y) l(x), \quad x, y \in S,\] for $k, l : S\rightarrow \mathbb{C}$, where $S$ is a…

We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic…

Let $ACC \circ THR$ be the class of constant-depth circuits comprised of AND, OR, and MOD$m$ gates (for some constant $m > 1$), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen…