Max Dehn Seminar
on Geometry, Topology, Dynamics, and Groups
Spring 2012
Date  Speaker  Title — click for abstract (if available)  
January 18 
Jon Chaika University of Chicago 
Badly approximable directions on flat surfaces
In this talk we show that directions on flat surfaces which are
poorly approximated by saddle connection directions are a
winning set for Schmidt's game. This extends a result of
Schmidt for the torus and strengthens a result of Kleinbock and
Weiss. We will state some consequences of the result. This is
joint work with Yitwah Cheung and Howard Masur.


February 1 
Chris Leininger UIUC 
Mapping class groups, Kleinian groups and convex cocompactness
For mapping class groups there is a notion of convex
cocompactness, due to Farb and Mosher, defined by way of
analogy with the concept of the same name in Kleinian groups.
On the other hand, there are certain Kleinian groups which can
themselves naturally be thought of as subgroups of mapping
class groups. After describing some of the background, I
will discuss a direct relationship between convex
cocompactness in the two settings for this special class of
groups. This is joint work with Spencer Dowdall and Richard
Kent.


February 16 Thursday, 2:30pm JWB 333 
Richard Hain Duke 
The Torelli group in genus 3
Thirty years ago Dennis Johnson proved that the Torelli group
\(T_g\) in genus g is finitely generated for all \(g \ge 3\).
Recently Putman initiated a program to give a new proof of
Johnson's fundamental result by proving that if \(T_3\) is
finitely generated, then so is \(T_g\) for all \(g > 3\). In
this talk I will explain why \(T_3\) is finitely generated, which
I will do in the more general context of understanding
fundamental groups of a certain class of branched coverings of
quasiprojective varieties having a complete Kaehler metric
with nonpositive sectional curvatures. I will also discuss the
problem of determining whether \(T_3\) is finitely presented. The
principal tool in the proof of the finite generation result and
the investigation of \(H_2(T_3)\) is the stratified Morse theory
of Goresky and MacPherson.


March 7 
Chris Atkinson Temple University 
Small volume link orbifolds
We will discuss recent joint work with Dave Futer in which we
study hyperbolic 3orbifolds having singular locus a link. We
have identified the smallest volume hyperbolic 3orbifold having
base space the 3sphere and singular locus a knot. We also
identify the smallest volume hyperbolic 3orbifold with base space
any homology 3sphere and singular locus a link. With weaker
homology assumptions, we obtain a lower bound on the volume of a
link orbifold.


March 14  Spring Break  No Talk  
March 28 
Ken Bromberg University of Utah 
TBA  
April 11 
Howard Masur University of Chicago 
Counting problems in the mapping class group
Let S be a surface of genus g with n punctures. Let Mod(S) the
mapping class group. It acts on T(S), the Teichmuller space of S
by isometries with respect to the Teichmuller metric. The action
is properly discontinuous. There are various counting problems
associated with this action. One of which is the lattice counting
problem which asks, given a pair of points x,y and a large number
r, how many elements of Mod(S) send y into a ball of radius r
centered at x. Athreyev, Bufetov, Eskin and Mirzakhani found
precise asymptotics of the form \( ce^{(6g6+n)r}\) for the
number as r goes to infinity. Maher showed that "most" such
elements are pseudoAnosov. I will give a quantitative version
by showing that the number that are not pseudoAnosov have
strictly smaller exponential growth.


April 25 
Brian Rushton Brigham Young University 
CANCELED 
Current seminar Archive of past talks
Max Dehn Seminar is organized by Mladen Bestvina, Ken Bromberg, Patrick Reynolds,
Jing Tao, Domingo Toledo, and Kevin Wortman.
This web page is maintained by Patrick Reynolds and Jing Tao.