Sets that are very large and very small
Abstract
Model companions of fields with no points in hyperbolic varieties
Abstract
This talk is based on a joint work with Vincent Jinhe Ye. I will define various classes of hyperbolic varieties (Broody hyperbolic, algebraically hyperbolic, bounded, groupless) and discuss existence of model companions of classes of fields that exclude them. This is related to moduli spaces of maps to hyperbolic varieties and to the (open) question whether the above mentioned hyperbolicity notions are in fact equivalent.
15:00
Mapping class group orbit closures for non-orientable surfaces
Abstract
The space of measured laminations on a hyperbolic surface is a generalisation of the set of weighted multi curves. The action of the mapping class group on this space is an important tool in the study of the geometry of the surface.
For orientable surfaces, orbit closures are now well-understood and were classified by Lindenstrauss and Mirzakhani. In particular, it is one of the pillars of Mirzakhani’s curve counting theorems.
For non-orientable surfaces, the behaviour of this action is very different and the classification fails. In this talk I will review some of these differences and describe mapping class group orbit closures of (projective) measured laminations for non-orientable surfaces. This is joint work with Erlandsson, Gendulphe and Souto.