Curves, Hyperbolicity, And Teichmüller Spaces (CHATS)

A day on low-dimensional geometric topology

Poster

Poster
cats by @神券涨涨的

Schedule

TimeSpeakerTitle
09:30–10:00Welcome & Coffee
10:00–11:00Suzanne SchlichBowditch representations in Gromov-hyperbolic spaces
11:00–11:30Coffee Break
11:30–12:30Ferrán ValdezBig mapping classes à la Denjoy and à la Penner
12:30–14:00Lunch
14:00–15:00Nolwenn Le QuellecUshijima coordinates and rigidity of the (simple) orthospectrum
15:00–15:30Coffee Break
15:30–16:30Mladen BestvinaTowards the Nielsen-Thurston classification for surfaces of infinite type

Titles and Abstracts

Mladen Bestvina — Towards the Nielsen-Thurston classification for surfaces of infinite type

Abstract: The fundamental theorem of Thurston states that any homeomorphism of a surface of finite type can be isotoped so that some multi-curve is invariant and so that for every complementary component the first return map is either periodic or pseudo-Anosov. Homeomorphisms of infinite type surfaces are much more complicated. In this work we focus on the class of tempered homeomorphisms -- these are the ones that do not have any mixing behavior. We show that up to isotopy there is an invariant geodesic lamination so that the first return maps display one of three qualitatively different behaviors. This work is joint with Federica Fanoni and Jing Tao.

Nolwenn Le Quellec — Ushijima coordinates and rigidity of the (simple) orthospectrum

Abstract: In 1993 Basmajian introduces the orthospectrum: the multiset of lengths of orthogeodesics on a hyperbolic surface with boundary. Moreover we define the simple orthospectrum as the multiset of lengths of orthogeodesics without self-intersection. Masai and McShane studied the question "Does the orthospectrum determine, up to isometry, a hyperbolic surface?", they gave an answer and a result of rigidity for surfaces with only one boundary component.
On another note, hyperbolic surfaces live in the Teichmüller space, which is usually described with Fenchel-Nielsen coordinates. In this talk, we will see how for hyperbolic surfaces with boundary we can use a different set of coordinates to study the rigidity of the orthospectrum and the simple orthospectrum and extend Masai and McShane's results: Ushijima coordinates.

Suzanne Schlich — Bowditch representations in Gromov-hyperbolic spaces

Abstract: Bowditch, followed by Tan-Wong-Zhang, introduced in 1998 a class of representations of the once-punctured torus group into PSL(2,C). Using trace relations in PSL(2,C), they give a condition on a representation which ensures that the translation lengths of the images of simple closed curves grow linearly with respect to the word length. In this talk, I will explain how to define and study a generalization of these conditions in the context of Gromov-hyperbolic spaces, where no trace relations hold, and give several characterizations of this set. I will also explain how this work makes it possible to study the dynamics of the mapping class group on the space of Bowditch representations.

Ferrán Valdez — Big mapping classes à la Denjoy and à la Penner

Abstract: In this talk we discuss homeomorphisms of big surfaces related to Denjoy homeomorphisms of the circle and products of weighted Dehn twists inspired by Penner's examples of pseudo-Anosov homeomorphisms. The discussion focuses on mapping torii and action on Teichmueller space.
This is joint work on one hand with Hernández-Hernández & Leininger, and on the other with Cremaschi & Souto.

Registration

Please register using the below form by 14th of May for coffee breaks and lunch count.

REGISTRATION IS NOW CLOSED. PLEASE CONTACT THE ORGANIZERS FOR A LATE REGISTRATION.

Practical Information

Location: UPEC, Amphi 3

Address: 61 Av. du Général de Gaulle, 94000 Créteil, France.

Date: 5th of June of 2026.

Travel:

Contact: david.fisac-camara@cnrs.fr, yusen.long@u-pec.fr

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