A dilation surface is a surface obtained from gluing Euclidean polygons along parallel sides (of possibly different lengths), and are in some sense generalisation of translation surfaces. These carry natural affine structures and foliations that we would like to understand.

In this talk I will explain a way to compactify the moduli space of such dilation surfaces using triangulations. This compactification is devised to account for dynamical properties of their directional foliations.

As an application of this compactification we prove the existence of infinitely many closed geodesics on any dilation surface.

Joint work with Adrien Boulanger and Guillaume Tahar.

https://umich.zoom.us/j/9660404387 Speaker(s): Selim Ghazouani (Orsay)