Min-max theory developed in the 80s by Pitts (using earlier work
of Almgren) allows one to construct closed embedded minimal
surfaces in 3-manifolds in great generality. The main challenge is
to understand the geometry of the limiting minimal...
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...
This talk will discuss the question: To what extent are the
fundamental groups of compact 3-manifolds determined (amongst the
fundamental groups of compact 3-manifolds) by their finite
quotients. We will discuss work that provides a positive
answer...
I will talk about bilipschitz geometry of complex algebraic
sets, focusing on the local geometry in dimension 2 (complex
surface singularities), where the topological classification has
long been understood in terms of 3-manifolds, while the...
Thurston's hyperbolization of fibered 3-manifolds is based on
his classification theorem for isotopy classes of surface
homeomorphisms. This classification has also been extremely
important to the study of dynamical systems on surfaces. The...
I will discuss a proof that a complete, non-compact hyperbolic
3- manifold $M$ with finite volume contains an immersed, closed,
quasi-Fuchsian surface that separates a given pair of points in the
sphere at infinity. Joint with David Futer.
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...
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...
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...
From a complex analytic perspective, Teichmüller spaces and
symmetric spaces can be realised as contractible bounded domains,
which have several features in common but also exhibit many
differences. In this talk we will study isometric maps
between...
