Orateur
Description
A translation surface is a surface endowed with
an atlas whose change of charts are translations. Fundamental
examples include the flat tori $\mathbb{C} / \Lambda$. A translation
surface comes with a one-parameter family of linear flows, one
for each direction in $\mathbb{C}$. Translation surfaces naturally
appear when considering billiard flows in rational polygons.
The main focus of the talk are the
$\operatorname{GL}^+_2(\mathbb{R})$-action on the moduli space
of translation surfaces and the multi-scale compactification
of $\operatorname{GL}^+_2(\mathbb{R})$-orbit closures.
After presenting the relevance of
$\operatorname{GL}^+_2(\mathbb{R})$-orbit closures in the
understanding of linear flows, I will describe how these
objects are amenable to efficient computations (in the sense
of computer programs).
This talk will be based on joint works with Julian Rüth, Kai Fu
and Bradley Zykoski.
