This presentation is meant as an extended version of the summary of my

work I gave for a New Guests' Oberseminar some months ago. The first

part will be a condensed account of Teichmüller spaces, mapping class

groups of surfaces, and how one uses coarse models (the curve graph, the

marking graph, the pants graph) to get a better understanding of them.

Then I will introduce train tracks - 'drawings' on the given surface

which look like railway networks - and the dynamics generated by their

splitting sequences: I will focus on how they fit in the

coarse-geometrical study of Teichmüller theory as they give tangible

examples of quasi-geodesic sequences. This will be an occasion to state

the main result of my PhD thesis - quasi-geodicity of splitting

sequences in the pants graph - and to say a few words about its proof.

Finally, if time allows, I will mention some connections of these topics

with the geometry of 3-manifolds and/or interesting questions I am

considering for my current and future work.

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