### List of speakers and titles

**Daniele Alessandrini:**The horofunction compactification of Teichmüller spaces of surfaces with boundary**Thomas Haettel:**Chabauty and horofunction compactifications.**Lizhen Ji:**Compactifications and modular interpretation of symmetric spaces.**Linus Kramer:**Rigidity of group topologie.**Cormac Walsh:**The horofunction compactification of symmetric cones.

Unfortunately, the talk of Amaury Thuillier (Compactifications of Bruhat-Tits buildings coming from Berkovich geometry) had to be canceled.

### Abstracts

#### Daniele Alessandrini: The horofunction compactification of Teichmüller spaces of surfaces with boundary

The Teichmüller space of surfaces with boundary can be equipped with an asymmetric distance, the arc distance, that generalizes Thurston asymmetric metric. In this talk I will describe the horofunction compactification of this distance and I will show that it coincides with Thurston's compactification of Teichmüller spaces. This is joint work with Lixin Liu, Athanase Papadopoulos and Weixu Su.

#### Thomas Haettel: Chabauty and horofunction compactifications

We will present an overview of two natural compactifications of various spaces. We will first discuss the Chabauty compactifications of homogeneous spaces, and consider the particular case of symmetric spaces and their spaces of maximal flats. We will then discuss the horofunction compactifications of metric spaces, and consider the particular case of symmetric spaces with various Finsler metrics (joint work with Anna Schilling and Anna Wienhard).

#### Lizhen Ji: Compactifications and modular interpretation of symmetric spaces

The analogy between symmetric spaces and moduli spaces is classical and fruitful. Many questions and results about moduli spaces of Riemann surfaces and Teichmuller spaces were motivated by those about locally symmetric spaces and symmetric spaces. We will discuss several results on compactifications of locally symmetric spaces and symmetric spaces in the opposite direction.

#### Linus Kramer: Rigidity of group topologies

We present old an new results on automatic continuity of 'abstract' homomorphisms between topological groups, with an emphasis on Lie groups, Polish groups, and locally compact groups. The problem itself was originally motivated by a geometric question about CAT(0) spaces. (This is partially joint work with O. Braun und K.H. Hofmann)

#### Cormac Walsh: The horofunction compactification of symmetric cones

Symmetric cones are examples of non-compact symmetric spaces. In this setting, it is usual to consider the Riemannian metric, but one can also take an invariant Finsler metric. In particular, on symmetric cones, the metrics of Hilbert and Thompson are very natural. I will discuss the horofunction compactification that arises when one uses either of these two metrics.

Here is a list of the abtracts of the talks as a pdf-file.

### Schedule

Beside the (public) talks there will be two plenary sessions and two groups discussions. In the first plenary session on Tuesday we want to collect open problems and interesting questions and group them for the discussions. In the group discussions on Wednesday the goal is to talk about some of the questions collected the day before in small groups. The workshop ends with a final plenary session where we present the material collected during these two days.

Here you can find a detailed schedule.