22 citations · 72 across the 26 of their papers we have counts for
28 papers
On the kissing number of hyperbolic surfaces with a small systole
S. Barré, M. Pichot
Parlier proved that there exists a constant such that for any hyperbolic surface of genus with systole the following holds: \[ Kiss(S)\leq U \frac {e^\ell}\ell…
Quasi-periodicity and almost equality classes
Mikael Pichot
We discuss the almost stability theorem of Dicks and Dunwoody in the context of probability measure preserving equivalence relations.
The Hamiltonian surface of $\Aut(F_2)$
Sylvain Barré, Mikaël Pichot
The group of automorphisms of the free group on two generators is known to act geometrically, in an essentially unique way, on a 2-dimensional CAT(0) space X. We prove that X conta…
On the classification of CW complexes with prescribed links
Sylvain Barré, Mikaël Pichot
Reporting on a computer--assisted search for nonpositively curved CW complexes of intermediate rank conducted some years ago. Not intended for publication.
The odd triangle ring puzzle problem
Sylvain Barré, Othmane Oukrid, Mikaël Pichot
Ring puzzles are tessellations of the Euclidean plane respecting local constraints around vertices. Such puzzles may arise in geometric group theory, for example, as embedded flat…
Separation theorems for bounded convex sets of bounded operators
Mikaël Pichot, Erik Séguin
We establish new metric characterizations for the norm (respectively, ultraweak) closure of the convex hull of a bounded set in an arbitrary -algebra (respectively, von Neuman…
Sidon sequences and nonpositive curvarture
Sylvain Barré, Mikaël Pichot
A sequence of nonnegative integers is called a Sidon sequence if the sums of pairs are all different. In this paper we construct CAT(0) groups and sp…
Positive definite maps on amenable groups, II
Mikaël Pichot, Erik Séguin
We introduce an Ulam-type stability condition for positive definite maps defined on a countable group and prove that this condition characterizes amenability.
Root distributions in Moebius-Kantor complexes
Sylvain Barré, Mikaël Pichot
We study the distribution of roots of rank 2 in nonpositively curved 2-complexes with Moebius--Kantor links. For every face in such a complex, the parity of the number of roots of…
Positive definite maps on amenable groups
Mikaël Pichot, Erik Séguin
We describe conditions that characterize amenability for groups in terms of positive definite functions valued in a von Neumann algebra.
Surgery on Aut(F2)
Sylvain Barre, Mikael Pichot
We study a geometric construction of certain finite index subgroups of Aut(F2).
Pauli matrices and ring puzzles
Sylvain Barre, Mikael Pichot
We study a family of tessellations of the Euclidean plane which are obtained by local developments of algebraic equations satisfied by the Pauli matrices.
A virtual geometric action of a braid group
Sylvain Barre, Mikael Pichot
We study a geometric action on a CAT(0) space of a finite index subgroup of the quotient group of the braid group on 4 strands by its center.
Isomorphisms and parity of complexes of rank 7/4
Sylvain Barre, Mikael Pichot
We study the isomorphism types of simply connected complexes of rank 7/4 using a local invariant called the parity. We show that the parity can be computed explicitly in certain co…
Random group cobordisms of rank 7/4
Sylvain Barre, Mikael Pichot
We construct a model of random groups of rank 7/4, and show that in this model the random group has the exponential mesoscopic rank property.
Surgery on discrete groups
Sylvain Barre, Mikael Pichot
We study constructions of groups, in particular of groups of intermediate rank, which are accessible to surgery techniques.
Universal entropy invariants
Robert Graham, Mikael Pichot
We define entropy invariants for abstract algebraic structures using an asymptotic Boltzmann formula.
A free product formula for the sofic dimension
Robert Graham, Mikael Pichot
It is proved that if is free product of probability measure preserving -regular ergodic discrete groupoids amalgamated over an amenable subgroupoid , then…
Random groups and nonarchimedean lattices
Sylvain Barre, Mikael Pichot
We consider models of random groups in which the typical group is of intermediate rank (in particular, it is not hyperbolic). These models are parallel to M. Gromov's well-known co…
An exotic group with the Haagerup property
Sylvain Barre, Mikael Pichot
We prove the Haagerup property for an infinite discrete group constructed using surgery on a Euclidean Tits building of type .
Sofic dimension for discrete measured groupoids
Ken Dykema, David Kerr, Mikael Pichot
For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations…
Orbit equivalence and sofic approximation
Ken Dykema, David Kerr, Mikael Pichot
Given an ergodic probability measure preserving dynamical system $\G\acts (X,μ)$, where $\G$ is a finitely generated countable group, we show that the asymptotic growth of the numb…
Closed manifolds with transcendental L2-Betti numbers
Mikaël Pichot, Thomas Schick, Andrzej Zuk
In this paper, we show how to construct examples of closed manifolds with explicitly computed irrational, even transcendental L2 Betti numbers, defined via the universal covering.…
Removing chambers in Bruhat-Tits buildings
Sylvain Barre, Mikael Pichot
We introduce and study a family of countable groups constructed from Euclidean buildings by "removing" suitably chosen subsets of chambers.