5 citations · 12 across the 15 of their papers we have counts for
20 papers
On the distribution of the components of multicurves of given type
Viveka Erlandsson, Juan Souto
We study the distribution of the individual components of a random multicurve under the action of the mapping class group.
Counting geodesics of given commutator length
Viveka Erlandsson, Juan Souto
Let be a closed hyperbolic surface. We study, for fixed , the asymptotics of the number of those periodic geodesics in having at most length and which can be written…
Counting and equidistribution of reciprocal geodesics and dihedral groups
Viveka Erlandsson, Juan Souto
We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL(2,R), generalizing earlier work of Sarnak and Bourgain-Kontorovich on the g…
Mapping class group orbit closures for non-orientable surfaces
Viveka Erlandsson, Matthieu Gendulphe, Irene Pasquinelli +1
Let be a connected non-orientable surface with negative Euler characteristic and of finite type. We describe the possible closures in and $\mathcal P\mat…
Distribution in the unit tangent bundle of the geodesics of given type
Viveka Erlandsson, Juan Souto
Recall that two geodesics in a negatively curved surface are of the same type if their free homotopy classes differ by a homeomorphism of the surface. In this note we study the…
Hyperbolic cone metrics and billiards
Viveka Erlandsson, Christopher J. Leininger, Chandrika Sadanand
A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complet…
Counting curves on orbifolds
Viveka Erlandsson, Juan Souto
We show that Mirzakhani's curve counting theorem also holds if we replace surfaces by orbifolds.
Genericity of pseudo-Anosov mapping classes, when seen as mapping classes
Viveka Erlandsson, Juan Souto, Jing Tao
We prove that pseudo-Anosov mapping classes are generic with respect to certain notions of genericity reflecting that we are dealing with mapping classes.
Mirzakhani's Curve Counting: From Simple to All
Viveka Erlandsson, Juan Souto
Mirzakhani obtained the asymptotic growth, when , of the number of curves in the mapping class group orbit of some given simple curve and with length at most . Years…
Ergodic invariant measures on the space of geodesic currents
Viveka Erlandsson, Gabriele Mondello
Let be a compact, connected, oriented surface, possibly with boundary, of negative Euler characteristic. In this article we extend Lindenstrauss-Mirzakhani's and Hamenstädt's c…
You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces
Moon Duchin, Viveka Erlandsson, Christopher J. Leininger +1
We give a complete characterization of the relationship between the shape of a Euclidean polygon and the symbolic dynamics of its billiard flow. We prove that the only pairs of tab…
Length functions on currents and applications to dynamics and counting
Viveka Erlandsson, Caglar Uyanik
The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of…
Counting curves, and the stable length of currents
Viveka Erlandsson, Hugo Parlier, Juan Souto
Let be a curve on a surface of genus and with boundary components and let be a discrete and cocompact action on some metric space. We s…
Short closed geodesics with self-intersections
Viveka Erlandsson, Hugo Parlier
Our main point of focus is the set of closed geodesics on hyperbolic surfaces. For any fixed integer , we are interested in the set of all closed geodesics with at least (bu…
A remark on the word length in surface groups
Viveka Erlandsson
Let be a surface of negative Euler characteristic and a generating set for consisting of simple loops that are pairwise disjoint (except at ). We show that th…
Simplicial embeddings between multicurve graphs
Viveka Erlandsson, Federica Fanoni
We study some graphs associated to a surface, called k-multicurve graphs, which interpolate between the curve complex and the pants graph. Our main result is that, under certain co…
Counting Curves in Hyperbolic Surfaces
Viveka Erlandsson, Juan Souto
Let be a hyperbolic surface. We study the set of curves on of a given type, i.e. in the mapping class group orbit of some fixed but otherwise arbitrary . For example,…
On Margulis cusps of hyperbolic 4-manifolds
Viveka Erlandsson, Saeed Zakeri
We study the geometry of the Margulis region associated with an irrational screw translation acting on the 4-dimensional real hyperbolic space. This is an invariant domain with…
The Margulis region and screw parabolic elements of bounded type
Viveka Erlandsson
Given a discrete subgroup of the isometries of n-dimensional hyperbolic space there is always a region kept precisely invariant under the stabilizer of a parabolic fixed point, cal…
Tame homomorphisms of polytopal rings
Viveka Erlandsson
The object of this paper is the tameness conjecture which describes an arbitrary graded k-algebra homomorphism of polytopal rings. We give further evidence of this conjecture by sh…