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Marie Trin

Publications and source records attributed to Marie Trin.

5 recordsLinked to original sources
arXiv2026

Large genus asymptotics for frequency of non-simple curves

We give an expression for the frequency of non-simple curves in closed surfaces and exploit it to study relative frequencies of such curves in large genus. This extend to the case of non-simple curves Mirzakhani's expressions of frequencies in terms of Konsevitch polynomials and Delecroix-Goujard-Zograf-Zorich large genus asymptotics for those frequencies. In particular, with K fixed, we identify which types of curves with K intersections are most common.

math.GT↗
arXiv2025

Stable subgroups of graph products

We extend the characterization of stable subgroups of right-angled Artin groups of Koberda, Mangahas and Taylor to the case of graph products of infinite groups. Specifically, we show that the stable subgroups of such graph products are exactly the subgroups that quasi-isometrically embed in the associated contact graph. Equivalently, they are the subgroups that satisfy a condition arising from the defining graph: a stable subgroup is an almost join-free subgroup. In particular, we generalize the equivalence between stable and purely loxodromic subgroups from Koberda, Mangahas and Taylor in the case where all torsion subgroups of the vertex groups are finite, and the equivalence between stable and infinite index Morse subgroups from Tran in the case where the defining graph is connected.

math.GR↗
arXiv2023

(Non-)Recognizing Spaces for Stable Subgroups

In this note, we consider the notion of what we call recognizing spaces for stable subgroups of a given group. When a group $G$ is a mapping class group or right-angled Artin group, it is known that a subgroup is stable exactly when the largest acylindrical action $G \curvearrowright X$ provides a quasi-isometric embedding of the subgroup into $X$ via the orbit map. In this sense the largest acylindrical action for mapping class groups and right-angled Artin groups provides a recognizing space for all stable subgroups. In contrast, we construct an acylindrically hyperbolic group (relatively hyperbolic, in fact) whose largest acylindrical action does not recognize all stable subgroups.

math.GR↗
arXiv2023

Counting arcs of the same type

We prove a general counting result for arcs of the same type in compact surfaces. Wealso count infinite arcs in cusped surfaces and arcs in orbifolds. These theorems are derived from aresult that guarantees the convergence of certain measures on the space of geodesic currents.

math.GT↗