Orateur
Description
In this expository survey talk, we will begin by recalling the Deligne-Mumford compactification of the moduli space of Riemann surfaces of fixed genus. Building on this, we will discuss the topic of compactifications of strata of differentials on Riemann surfaces (i.e. spaces of translation surfaces), which has seen intense activity in the last decade, and which will play an important role in several later talks at this conference. We will take a tour of these compactifications, discussing constructions, examples, and applications, mainly from the perspective of flat geometry. In particular, we will consider the "What You See Is What You Get" compactification studied by Mirzakhani-Wright, and the Multi-scale compactification constructed by Bainbridge-Chen-Gendron-Grushevsky-Moller.
