39 citations · 85 across the 15 of their papers we have counts for
26 papers
Spectral gaps of double covers of hyperbolic surfaces
Lawford Hatcher, Bram Petri
We prove that, in most moduli spaces of orientable hyperbolic surfaces of finite area, there exist surfaces all of whose covers of degree two have a new small eigenvalue. On the ot…
A sharper bound on the minimal possible diameter of a closed hyperbolic surface
Joffrey Mathien, Bram Petri
We prove that the minimal possible diameter of a closed hyperbolic surface of genus is at most .
Random surfaces with large systoles
Mingkun Liu, Bram Petri
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their are…
Linear programming bounds for hyperbolic surfaces
Maxime Fortier Bourque, Bram Petri
We adapt linear programming methods from sphere packings to closed hyperbolic surfaces and obtain new upper bounds on their systole, their kissing number, the first positive eigenv…
On Cheeger constants of hyperbolic surfaces
Thomas Budzinski, Nicolas Curien, Bram Petri
It is a well-known result due to Bollobas that the maximal Cheeger constant of large -regular graphs cannot be close to the Cheeger constant of the -regular tree. We prove an…
The Klein quartic maximizes the multiplicity of the first positive eigenvalue of the Laplacian
Maxime Fortier Bourque, Bram Petri
We prove that Klein quartic maximizes the multiplicity of the first positive eigenvalue of the Laplacian among all closed hyperbolic surfaces of genus , with multiplicity equal…
A model for random three--manifolds
Bram Petri, Jean Raimbault
We study compact three-manifolds with boundary obtained by randomly gluing together truncated tetrahedra along their faces. We prove that, asymptotically almost surely as the numbe…
Statistics of finite degree covers of torus knot complements
Elizabeth Baker, Bram Petri
In the first part of this paper, we determine the asymptotic subgroup growth of the fundamental group of a torus knot complement. In the second part, we use this to study random fi…
The diameter of random Belyi surfaces
Thomas Budzinski, Nicolas Curien, Bram Petri
We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of hyperbo…
Kissing numbers of regular graphs
Maxime Fortier Bourque, Bram Petri
We prove a sharp upper bound on the number of shortest cycles contained inside any connected graph in terms of its number of vertices, girth, and maximal degree. Equality holds onl…
On the minimal diameter of closed hyperbolic surfaces
Thomas Budzinski, Nicolas Curien, Bram Petri
We prove that the minimal diameter of a hyperbolic compact orientable surface of genus is asymptotic to as . The proof relies on a random construction, w…
Kissing numbers of closed hyperbolic manifolds
Maxime Fortier Bourque, Bram Petri
We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold of any dimension in terms of its volume and systole, generalizing a theorem of P…
Universality for random surfaces in unconstrained genus
Thomas Budzinski, Nicolas Curien, Bram Petri
Starting from an arbitrary sequence of polygons whose total perimeter is , we can build an (oriented) surface by pairing their sides in a uniform fashion. Chmutov and Pittel (a…
On distinct finite covers of 3-manifolds
Stefan Friedl, JungHwan Park, Bram Petri +2
Every closed orientable surface S has the following property: any two connected covers of S of the same degree are homeomorphic (as spaces). In this, paper we give a complete class…
Subgroup growth of virtually cyclic right-angled Coxeter groups and their free products
Hyungryul Baik, Bram Petri, Jean Raimbault
We determine the asymptotic number of index subgroups in virtually cyclic right-angled Coxeter groups and their free products as .
Subgroup growth of right-angled Artin and Coxeter groups
Hyungryul Baik, Bram Petri, Jean Raimbault
We determine the factorial growth rate of the number of finite index subgroups of right-angled Artin groups as a function of the index. This turns out to depend solely on the indep…
Lengths of closed geodesics on random surfaces of large genus
Maryam Mirzakhani, Bram Petri
We prove Poisson approximation results for the bottom part of the length spectrum of a random closed hyperbolic surface of large genus. Here, a random hyperbolic surface is a surfa…
Counting non-commensurable hyperbolic manifolds and a bound on homological torsion
Bram Petri
We prove that the cardinality of the torsion subgroups in homology of a closed hyperbolic manifold of any dimension can be bounded by a doubly exponential function of its diameter.…
Hyperbolic surfaces with long systoles that form a pants decomposition
Bram Petri
We present a construction of sequences of closed hyperbolic surfaces that have long systoles which form pants decompositions of these surfaces. The length of the systoles of these…
Exponential Torsion Growth for Random 3-Manifolds
Hyungryul Baik, David Bauer, Ilya Gekhtman +5
We show that a random 3-manifold with positive first Betti number admits a tower of cyclic covers with exponential torsion growth.
Poisson approximation of the length spectrum of random surfaces
Bram Petri, Christoph Thaele
Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds i…
Mapping class group orbits of curves with self-intersections
Patricia Cahn, Federica Fanoni, Bram Petri
We study mapping class group orbits of homotopy and isotopy classes of curves with self-intersections. We exhibit the asymptotics of the number of such orbits of curves with a boun…
Graphs of Large Girth and Surfaces of Large Systole
Bram Petri, Alexander Walker
The systole of a hyperbolic surface is bounded by a logarithmic function of its genus. This bound is sharp, in that there exist sequences of surfaces with genera tending to infinit…
The genus of curve, pants and flip graphs
Hugo Parlier, Bram Petri
This article is about the graph genus of certain well studied graphs in surface theory: the curve, pants and flip graphs. We study both the genus of these graphs and the genus of t…