Related papers: The Dehn Function of PSL(2,Z[1/p])

We define Ptolemy coordinates for representations that are not necessarily boundary-unipotent. This gives rise to a new algorithm for computing the SL(2,C) A-polynomial, and more generally the SL(n,C) A-varieties. We also give a formula for…

We compute the $\text{PSL}(2,\mathbb{C})$ Chern-Simons partition function of a closed 3-manifold obtained from Dehn fillings of the link complement $\mathbf S^3\backslash {\mathcal{L}}$, where $\mathcal{L}=\mathcal{K}# H$ is the connected…

Given an abstract group $G$, we study the function $ab_n(G) := \sup_{|G:H| \leq n} |H/[H,H]|$. If $G$ has no abelian composition factors, then $ab_n(G)$ is bounded by a polynomial: as a consequence, we find a sharp upper bound for the…

Let $p(n)$ denote the partition function. In this paper our main goal is to derive an asymptotic expansion up to order $N$ (for any fixed positive integer $N$) along with estimates for error bounds for the shifted quotient of the partition…

Let x be a random vector coming from any k-wise independent distribution over {-1,1}^n. For an n-variate degree-2 polynomial p, we prove that E[sgn(p(x))] is determined up to an additive epsilon for k = poly(1/epsilon). This answers an open…

In this paper, we study the existence and uniqueness of $\mathbb{L}^p$-solutions for $p \in (1, 2)$, first for backward stochastic differential equations (BSDEs) in a general filtration that supports a Brownian motion and an independent…

Let $p(n)$ denote the partition function and define $p(n,k)=\sum_{j=0}^{k}\binom{n-j}{k-j}p(j)$ where $p(0)=1$. We prove that $p(n,k)$ is unimodal and satisfies $p(n,k) < \frac{2.825}{\sqrt{n}}\, 2^n $ for fixed $n\ge 1$ and all $1\le k\le…

We prove the Kloosterman-Spectral sum formula for PSL(2,Z[i])\PSL(2,C), and apply it to derive an explicit spectral expansion for the fourth power moment of the Dedekind zeta function of the Gaussian number field. This sum formula allows…

We study the L^p-distortion of finite quotients of amenable groups. In particular, for every number p larger or equal than 2, we prove that the l^p-distortion of the finite lamplighter group grows like (\log n)^{1/p}. We also give the…

We define a necessary and sufficient condition on a polynomial $h\in \mathbb{Z}[x]$ to guarantee that every set of natural numbers of positive upper density contains a nonzero difference of the form $h(p)$ for some prime $p$. Moreover, we…

We present an algorithm for computing the Lyndon factorization of a string that is given in grammar compressed form, namely, a Straight Line Program (SLP). The algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space, where $m$ is the…

We consider the continued fraction expansion of real numbers under the action of a non-uniform lattice in PSL(2,R) and prove metric relations between the convergents and a natural geometric notion of good approximations.

We construct and study finitely presented groups with quadratic Dehn function (QD-groups) and present the following applications of the method developed in our recent papers. (1) The isomorphism problem is undecidable in the class of…

We describe the orbits of the irreducible action of PSL(2, R) on the 3-dimensional Einstein universe Ein 1,2. This work completes the study in [2], and is one element of the classification of cohomo-geneity one actions on Ein 1,2 ([5]).

We analyze the Fourier growth, i.e. the $L_1$ Fourier weight at level $k$ (denoted $L_{1,k}$), of various well-studied classes of "structured" $\mathbb{F}_2$-polynomials. This study is motivated by applications in pseudorandomness, in…

We present a way to construct Parseval frames of piecewise constant functions for $L^2[0,1]$. The construction is similar to the generalized Walsh bases. It is based on iteration of operators that satisfy a Cuntz-type relation, but without…

For a finitely presented group, the word problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is a complexity measure of a direct attack on the word problem by…

Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees…

The representation of the conformal group (PSU(2,2)) on the space of solutions to Maxwell's equations on the conformal compactification of Minkowski space is shown to break up into four irreducible unitarizable smooth Fr\'echet…

Let $f$ be a function on ${\Bbb R}^2$ in the inhomogeneous Besov space $B_{\infty,1}^1({\Bbb R}^2)$. For a pair $(A,B)$ of not necessarily bounded and not necessarily commuting self-adjoint operators, we define the function $f(A,B)$ of $A$…