Special Year 2015-16: Geometric Structures on 3-manifolds - Seminar

We consider questions that arise naturally from the subject of the first talk. The have two main results: 1. In genus $g$, the algebraic degrees of pseudo-Anosov stretch factors include all even numbers between $2$ and $6g - 6$; 2. The Galois...

In this first talk, we give an introduction to Penner’s construction of pseudo-Anosov mapping classes. Penner conjectured that all pseudo-Anosov maps arise from this construction up to finite power. We give an elementary proof (joint with Hyunshik...

Let $G$ be a group acting by isometries on a Gromov hyperbolic space, which need not be proper. If $G$ contains two hyperbolic elements with disjoint fixed points, then we show that a random walk on $G$ converges to the boundary almost surely. This...

We give a brief introduction to random walks on groups with hyperbolic properties.

We prove that if a hyperbolic group $G$ acts cocompactly on a CAT(0) cube complexes and the cell stabilizers are quasiconvex and virtually special, then $G$ is virtually special. This generalizes Agol's Theorem (the case when the action is proper)...

Sageev associated to a codimension 1 subgroup $H$ of a group $G$ a cube complex on which $G$ acts by isometries, and proved this cube complex is always CAT(0). Haglund and Wise developed a theory of special cube complexes, whose fundamental groups...

The non-orientable genus (a.k.a crosscap number) of a knot is the smallest genus over all non-orientable surfaces spanned by the knot. In this talk, I’ll describe joint work with Christine Lee, in which we obtain two-sided linear bound of the...

We will discuss methods of decomposing knot and link complements into polyhedra. Using hyperbolic geometry, angled structures, and normal surface theory, we analyze geometric and topological properties of knots and links.

Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional $\mathbf{Z}/2$ vector space. The main result about the instanton homology is a non-vanishing theorem, proved using techniques...