Geometry Titles and Abstracts

Titles and Abstracts

Michelle Chu

Virtual properties of arithmetic hyperbolic 3-manifolds

The virtually special theorems of Agol and Wise tell us that hyperbolic 3-manifold groups virtually embed as subgroups of right-angled Coxeter groups, and as such, inherit many interesting virtual properties. In this talk I will focus on a particular class of arithmetic hyperbolic 3-manifold groups and discuss how explicit embeddings into reflection groups of hyperbolic Coxeter polytopes can provide more nuanced data on some of these virtual properties.

Annette Karrer

Contracting boundaries of right-angled Coxeter groups

A complete CAT(0) space has a topological space associated to it called the contracting or Morse boundary. This boundary captures how similar the CAT(0) space is to a hyperbolic space. Charney--Sultan proved this boundary is a quasi-isometry invariant, i.e. it can be defined for CAT(0) groups. Interesting examples arise among contracting boundaries of right-anlged Coxeter groups.

The talk will consist of two parts. The main part will be about my PhD project. We will study the question of how the contracting boundary of a right-angled Coxeter group changes when we glue certain graphs on its defining graph. We will focus on the question of when the resulting graph corresponds to a right-angled Coxeter group with totally disconnected contracting boundary. Afterward, we will discuss surprising circles in contracting boundaries of certain RACGs. The latter is joint work with Marius Graeber, Nir Lazarovich, and Emily Stark.

Mireille Soergel

Dyer groups

One common feature of Coxeter groups and right-angled Artin groups is their solution to the word problem. In his study of reflection subgroups of Coxeter groups, Dyer introduces a family of groups, Dyer groups, which also have the same solution to the word problem as Coxeter groups. I will introduce this family of groups, give some of their properties

Yuri Santos Rego

Exploring the Coxeter galaxy

In this talk we will pull out our telescopes to have a look at the galaxy of Coxeter groups, which is a portion of the universe of finitely presented groups encoding Coxeter groups up to isomorphism. We shall discuss tools to chart the Coxeter galaxy and discuss the parts that humankind has explored so far.