Alice Mark

activity

20122023

most citedPresentations for cusped arithmetic hyperbolic lattices

5 citations · 8 across the 4 of their papers we have counts for

collaborators

6 papers

math.CO2023★ 1 cited

Shi arrangements and low elements in Coxeter groups

Matthew Dyer, Christophe Hohlweg, Susanna Fishel +1

Given an arbitrary Coxeter system $(W, S)$ and a nonnegative integer $m$ , the $m$ -Shi arrangement of $(W, S)$ is a subarrangement of the Coxeter hyperplane arrangement of $(W, S)$ . Th…

math.GR2021

Picard modular groups generated by complex reflections

Alice Mark, Julien Paupert, David Polletta

In this short note we use the presentations found in \cite{MP} and \cite{Po} to show that the Picard modular groups $PU (2, 1, O_{d})$ with $d = 1, 3, 7$ (respectively the q…

math.GR2017★ 5 cited

Presentations for cusped arithmetic hyperbolic lattices

Alice Mark, Julien Paupert

We present a general method to compute a presentation for any cusped arithmetic hyperbolic lattice $Γ$ , applying a classical result of Macbeath to a suitable $Γ$ -invariant horoball…

math.GR2015★ 2 cited

The classification of Rank 3 Reflective Hyperbolic Lattices over Z[\sqrt{2}]

Alice Mark

There are 432 strongly squarefree symmetric bilinear forms of signature $(2, 1)$ defined over $Z [2]$ whose integral isometry groups are generated up to finite index by finit…

math.NT2015

The Conway-Sloane calculus for 2-adic lattices

Daniel Allcock, Itamar Gal, Alice Mark

We motivate and explain the system introduced by Conway and Sloane for working with quadratic forms over the 2-adic integers, and prove its validity. Their system is far better for…

math.GR2012

Reflection groups of the quadratic form -px_0^2+x_1^2+...+x_n^2

Alice Mark

We present the classification of reflective quadratic forms $- p x_{0}^{2} + x_{1}^{2} + \dots + x_{n}^{2}$ for $p$ prime. We show that for $p = 5$ , it is reflective for $2 \leq n \leq 8$ , for $p = 7\t…