9 citations · 36 across the 16 of their papers we have counts for
19 papers
FAMED by computer: proving the Andersen-Kashaev volume conjecture for 42,000 knots
Fathi Ben Aribi, Antonin Guilloux, Ka Ho Wong
The FAMED condition is a combinatorial property for ideal triangulations of -manifolds, which was introduced in 2024 by the first and last authors in order to study the Andersen…
Limits of limit sets in rank-one symmetric spaces
Antonin Guilloux, Theodore Weisman
We consider the question of continuity of limit sets for sequences of geometrically finite subgroups of isometry groups of rank-one symmetric spaces, and prove analogues of classic…
A Hilbert metric for bounded symmetric domains
Elisha Falbel, Antonin Guilloux, Pierre Will
Bounded symmetric domains carry several natural invariant metrics, for example the Carathéodory, Kobayashi or the Bergman metric. We define another natural metric, from generalized…
Slim curves, limit sets and spherical CR uniformisations
Elisha Falbel, Antonin Guilloux, Pierre Will
We consider here the -sphere seen as the boundary at infinity of the complex hyperbolic plane . It comes equipped with a contact structur…
Limits of Mahler measures in multiple variables
François Brunault, Antonin Guilloux, Mahya Mehrabdollahei +1
We prove that certain sequences of Laurent polynomials, obtained from a fixed Laurent polynomial P by monomial substitutions, give rise to sequences of Mahler measures which conver…
Deformation space of discrete groups of SU(2,1) in quaternionic hyperbolic plane
Antonin Guilloux, Inkang Kim
In this note, we study deformations of discrete and Zariski dense subgroups of SU(2, 1) in quaternionic hyperbolic space. Specifi- cally we consider two examples coming from repres…
Hilbert metric, beyond convexity
Elisha Falbel, Antonin Guilloux, Pierre Will
The Hilbert metric on convex subsets of has proven a rich notion and has been extensively studied. We propose here a generalization of this metric to subset of comple…
Volume function and Mahler measure of exact polynomials
Antonin Guilloux, Julien Marché
We study a class of 2-variable polynomials called exact polynomials which contains -polynomials of knot complements. The Mahler measure of these polynomials can be computed in t…
Yet another p-adic hyperbolic disc
Antonin Guilloux
We describe in this paper a geometric construction in the projective p-adic plane that gives, together with a suitable notion of p-adic convexity, some open subsets of P 2 .Q p / n…
Deformation of hyperbolic manifolds in and discreteness of the peripheral representations
Antonin Guilloux
Let be a cusped hyperbolic -manifold, e.g. a knot complement. Thurston showed that the space of deformations of its fundamental group in (u…
Equidistribution in S-arithmetic and adelic spaces
Antonin Guilloux
We give an introduction to adelic mixing and its applications for mathematicians knowing about the mixing of the geodesic flow on hyperbolic surfaces. We focus on the example of th…
On SL(3,)-representations of the Whitehead link group
Antonin Guilloux, Pierre Will
We describe a family of representations in SL(3,) of the fundamental group of the Whitehead link complement. These representations are obtained by considering pairs…
Volumes of representations and birationality of the peripheral holonomy
Antonin Guilloux
We discuss here a generalization of a theorem by Dunfield stating that the peripheral holonomy map, from the character variety of a 3-manifold to the A-polynomial is birational. Du…
Dimension of character varieties for -manifolds
Elisha Falbel, Antonin Guilloux
Let be a -manifold, compact with boundary and its fundamental group. Consider a complex reductive algebraic group G. The character variety is the GIT quotient $…
Character varieties for SL(3,C): the figure eight knot
Elisha Falbel, Antonin Guilloux, Pierre-Vincent Koseleff +2
We give a description of several representation varieties of the fundamental group of the complement of the figure eight knot in PGL(3,C) or SL(3,C). We moreover obtain an explicit…
Representations of 3-manifold groups in PGL(n,C) and their restriction to the boundary
Antonin Guilloux
We study here the space of representations of a fundamental group of a 3-manifold into PGL(n,C). Thurston, Neumann and Zagier initiated a strategy (in the case of PGL(2,C)) consist…
Local rigidity for PGL(3,C)-representations of 3-manifold groups
N. Bergeron, E. Falbel, A. Guilloux +2
Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by…
Polynomial dynamic and lattice orbits in S-arithmetic homogeneous spaces
Antonin Guilloux
Consider an homogeneous space under a locally compact group G and a lattice in G. Then the lattice naturally acts on the homogeneous space. Looking at a dense orbit, one may wonder…
A brief remark on orbits of in the euclidean plane
Antonin Guilloux
The repartition of dense orbits of $\textrm{SL}(2,\dr Z)$ in the euclidean plane is described by Ledrappier and Nogueira. We describe here the specific patterns one can see by expe…