Hugo Parlier

collaborators

9 papers

math.GT2026

The inf spectrum of moduli space

Ara Basmajian, Sayantika Mondal, Hugo Parlier

Given a surface of genus $g \geq 2$ , its inf spectrum is the ordered multiset of inf lengths of curves on the surface, the infimum being over all hyperbolic metrics. We show that t…

math.GT2026

A topological version of Huber's theorem

Ara Basmajian, Hugo Parlier

Let $X$ be a closed hyperbolic surface. We prove that the number of topological types of primitive closed geodesics of length at most $L$ is asymptotic to \[ \frac{1}{|\Isom(X)|}\f…

math.GT2026

The entropy spectrum of hyperbolic surfaces

Ara Basmajian, Hugo Parlier

This article introduces and studies the entropy spectrum of a hyperbolic surface, that is the set of entropies of its subsurfaces. The main results are that the entropy spectrum is…

math.GT2026

Counting and entropy for hyperbolic surface amalgams

Hugo Parlier, Yandi Wu

This paper is about closed hyperbolic surface amalgams with a focus on the growth of the number of closed geodesics. As in the case of surfaces, we show that topological and volume…

math.GT2026

The crossing number of polynomial curve systems

Sebastian Baader, Jasmin Jörg, Hugo Parlier

We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.

math.GT2026

Graded Bridgeman dilogarithm identities on hyperbolic surfaces

Ara Basmajian, Nhat Minh Doan, Hugo Parlier +1

We establish graded versions of Bridgeman's dilogarithm identity for hyperbolic cone surfaces, including surfaces with only cusps and cone points, and provide applications to the s…

math.GT2025

Near ideal decompositions of ideal polygons

Hugo Parlier

This article gives a short proof that all ideal polygons admit a short orthogeodesic decomposition. Specifically, all $n$ -gons admit an orthogeodesic decomposition with orthogeodes…

math.GT2025

Modular systoles are extremal for the crossing number

Claire Burrin, Hugo Parlier

We study crossing numbers for systoles of congruence surfaces. Taken as a family of curves on a family of surfaces, we show that the growth rate of their intersection is optimally…

math.GT2025

Flip-graphs of non-orientable filling surfaces

Pallavi Panda, Hugo Parlier, Lionel Pournin

Consider a surface $Σ$ with punctures that serve as marked points and at least one marked point on each boundary component. We build a filling surface $Σ_{n}$ by singling out one of…