A classical property of pseudo-Anosov mapping classes is that
they act on the space of projective measured laminations with
north-south dynamics. This means that under iteration of such a
mapping class, laminations converge exponentially quickly...
This is joint work with Thomas Barthelme of Penn State
University. There are Anosov and pseudo-Anosov flows so that some
orbits are freely homotopic to infinitely many other orbits. An
Anosov flow is $R$-covered if either the stable or unstable...
We prove that any right-angled Coxeter group on $k$ generators
admits a proper action by affine transformations on $\mathbb
R^{k(k-1)/2}$. As a corollary, many interesting groups admit proper
affine actions including surface groups, hyperbolic three...
The Min-max Theory for the area functional, started by Almgren
in the early 1960s and greatly improved by Pitts in 1981, was left
incomplete because it gave no Morse index estimate for the min-max
minimal hypersurface. Nothing was said also about...
I will talk about convex-cocompact representations of finitely
generated free group $F_g$ into $\mathrm{PSL}(2,\mathbb C)$. First
I will talk about Schottky criterion. There are many ways of
characterizes Schottky group. In particular, convex hull...
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...
