Through the work of Agol and Wise, we know that all closed
hyperbolic 3-manifolds are finitely covered by a surface bundle
over the circle. Thus the geometry of these bundles indicates the
geometry of general hyperbolic 3-manifolds. But there are...
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...
For this talk I'll discuss uniformization of Riemann surfaces
via Kleinian groups. In particular question of conformability by
Hasudorff dimension spectrum. I'll discuss and pose some questions
which also in particular will imply a conjecture due to...
A theorem of Borel's asserts that for any positive real number $V$,
there are at most finitely many arithmetic lattices in ${\rm
PSL}_2({\mathbb C})$ of covolume at most $V$, or equivalently at
most finitely many arithmetic hyperbolid $3$-orbifolds...
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...
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.
