### September 23

**Speaker:** Katherine Goldman

**Title: **CAT(0) cube complexes, right-angled Artin groups, and the virtual fibering conjecture for 3-manifolds Part I: Ingredients of the proof

**Abstract:**

One of the great theorems in 3-manifold theory is the virtual fibering conjecture (now theorem), which states that every (closed, atoroidal, irreducible, infinite fundamental group) 3-manifoldĀ has a finite cover which is a fiber bundle over the circle, with fiber a surface. The geometrization theorem implies the theorem for non-hyperbolic 3-manifolds, while the proof of the conjecture for hyperbolic 3-manifolds utilizes many prominent objects of study in Geometric Group Theory, including special/CAT(0) cube complexes and right-angled Artin groups. In this talk we will describe these ingredients of the proof for hyperbolic 3-manifolds and explain how they are used in tandem with the virtual Haken conjecture (now theorem; another major result) to prove the full virtual fibering conjecture.

### September 30

**Speaker:** Katherine Goldman

**Title: **CAT(0) cube complexes, right-angled Artin groups, and the virtual fibering conjecture for 3-manifolds Part II: Outline of the proof

**Abstract:**

After the general set up of last week, I will outline the proof with emphasis on the usage of CAT(0) cube complexes and right-angled Artin groups.

### October 7

**Speaker:** Hyeran Cho

**Title: **Relative hyperbolicity and Dehn fillings

**Abstract:**

For a compact 3-manifold with torus boundary, we obtain a closed 3-manifold by attaching a solid torus to the boundary. This topological operation is called Dehn filling of spaces. From the group theoretic point of view, we consider a Dehn filling of a group where the group is the fundamental group of a complete finite volume hyperbolic manifold. Also, we can generalize this to relative hyperbolic groups and consider their Dehn fillings.

In this talk, I would like to introduce hyperbolic groups and relative hyperbolic groups. Moreover, we would consider Dehn fillings of relatively hyperbolic groups.

### October 14

**No meeting–fall break**

### October 24 (New day of the week!)

**Speaker:** James Marshall Reber

**Title: **The Weil-Petersson Metric

**Abstract:**

In this talk, we will present the definition of the Weil-Petersson metric on Teichmuller space and describe some interesting results related to the metric.