Max Dehn Seminar
on Geometry, Topology, Dynamics, and Groups
Academic year 2009  2010
Date  Speaker  Title — click for abstract (if available) 
September 2, 2009 
Jing Tao University of Utah 
Linearly bounded conjugator property for mapping class groups
Given two conjugate mapping classes \(f\) and \(g\), we produce a
conjugating element \(w\) such that \(w \le K (f + g)\), where
\(\cdot\) denotes the word metric with respect to a fixed
generating set, and \(K\) is a constant depending only on the
generating set. As a consequence, the conjugacy problem for
mapping class groups is exponentially bounded.

September 9, 2009 
Mladen Bestvina University of Utah 
Asymptotic dimension of Mapping class groups
The first talk will review the concept of asymptotic dimension and
some background material. In the second talk I will construct (many)
actions of mapping class groups on quasitrees, and show how this
implies that mapping class groups have finite asymptotic dimension.
This is joint work with Ken Bromberg and Koji Fujiwara.

September 23, 2009 
Martin Deraux University of Grenoble I (Institut Fourier) 
Pinching questions for manifolds of negative curvature 
September 30, 2009 
Mladen Bestvina University of Utah 
Asymptotic dimension of Mapping class groups, cont.
The first talk will review the concept of asymptotic dimension and
some background material. In the second talk I will construct (many)
actions of mapping class groups on quasitrees, and show how this
implies that mapping class groups have finite asymptotic dimension.
This is joint work with Ken Bromberg and Koji Fujiwara.

October 7, 2009 
Christopher Cashen University of Utah 
Mapping Tori of Free Group Automorphisms and Line Patterns in Free Groups
I will talk about line patterns in free groups and how they
provide quasiisometry invariants for mapping tori of linearly
growing free group automorphisms. This is joint with Natasha
Macura.

October 28, 2009 
William Malone University of Utah 
Isometries of Products of Uniquely Geodesic Metric Spaces with the Sup Norm are Reducible
Let f be an isometry between spaces which are products of
uniquely geodesic metric spaces with the sup norm. There are
two obvious types of isometries from such a space to itself
namely a permutation of the factor spaces and a product of
isometries of the factor spaces. In this talk we will show
that not only is the number of factor spaces an isometry
invariant, but also that any isometry is a composition of the
two isometries types mentioned above.

November 11, 2009 
Yael AlgomKfir University of Utah 
Asymmetry of Outer Space
The Lipschitz metric on Outer Space is not symmetric. In fact
d(x,y)/d(y,x) can be arbitrarily large. In joint work with Mladen
Bestvina, we define a piecewise differentiable function \psi on Outer
Space (which is invariant under the action of Out(Fn) and show that d(x,y)
can be bounded in terms of d(y,x) and \psi(x)  \psi(y). I will discuss
the proof of this theorem and some applications.

November 18, 2009 
Kevin Wortman University of Utah 
Nonnonpositive curvature of some noncocompact arithmetic groups
I'll explain why arithmetic groups of relative Qtype A_n, B_n,
C_n, D_n, E_6, and E_7 satisfy an exponential isoperimetric
inequality in some dimension.

December 2, 2009 
Mladen Bestvina University of Utah 
A new proof of the train track theorem 
January 13, 2010 
Kasra Rafi University of Oklahoma 
Lengths of curves along a Teichmüller geodesic
We show that the extremal length and the hyperbolic length
of any simple closed curve are quasiconvex functions of time
along any Teichmüller geodesic. As a corollary, we
conclude that, in Teichmüller space equipped with the
Teichmüller metric, balls are quasiconvex.
(Joint work with Anna Lenzhen.)

January 27, 2010 
Juan Souto University of Michigan 
(Non)actions of the mapping class group on the unit tangent bundle.
By the work of Morita and Markovic, it is known that the
mapping class group of a surface $S$ does not act naturally on $S$.
However, such an action, by Hoelder homeomorphisms, exists on the unit
tangent bundle $T^1S$ of the surface. In this talk I will explain why
this last action is conjugated to a Lipschitz action but not even
homotopic to a smooth one.

January 29, 2010 
Alexandra Pettet University of Michigan 
Periodic maximal flats are not peripheral
I will prove that every finite volume locally symmetric space contains a
compact set K with the property that no periodic maximal flat can be
homotoped to be disjoint from K. This is joint work with Juan Souto.

February 3, 2010 
Jeno Szigeti Miskolc, Hungary 
Centralizers in Endomorphism Rings 
February 10, 2010 
Jing Tao University of Utah 
Teichmüller diameter of the thick part of moduli space
Let S be a closed surface of genus \( g \ge 2 \). The thick part of
the moduli space of S is the set of hyperbolic metrics on S such that
the length of the shortest loop is bounded below by a fixed constant.
We study the asymptotic behavior of the diameter of this set equipped
with the Teichmüller metric and prove that it grows like
\( \log(g) \). This is joint with Kasra Rafi.

March 3, 2010 
William Malone University of Utah 
Quasiisometric Classification of Geometric Amalgamations of Free Groups
In order to understand the large scale geometry of limit groups
a good starting place is with geometric amalgamations of free
groups (a class of graphs of groups) since they are virtually
limit groups. In this talk a complete quasiisometric
invariant for geometric amalgamations of free groups will be
given, along with an elementary example showing that
commensurability and quasiisometry are not the same
equivalence relation for virtual limit groups.

March 5, 2010 
John Parker Durham 
Constructing nonarithmetic lattices
The first examples of nonarithmetic complex hyperbolic lattices
were given by Mostow in 1980. These examples are generalised triangle
groups generated by complex reflections of orders 3, 4 or 5.
I will discuss how to parametrise such triangle groups and how to
identify which of them may possibly be lattices. Most of these
candidates are nonarithmetic. I will then survey an ongoing project
with Deraux and Paupert whose goal is to use this idea to construct
(families of) new nonarithmetic complex hyperbolic lattices.

March 10, 2010 
David Futer Temple University 
Bourdon's building and hyperbolic surfaces
Bourdon's building is a negatively curved 2complex built out
of hyperbolic rightangled polygons. Its automorphism group is
large (uncountable) and remarkably rich. We study, and mostly
answer, the question of when there is a discrete subgroup of
the automorphism group such that the quotient is a closed
surface of genus g. This involves some fun elementary
combinatorics, but quickly leads to open questions in group
theory and number theory. This is joint work with Anne Thomas.

March 17, 2010 
Anne Thomas University of Oxford 
Lattices in complete KacMoody groups
A complete KacMoody group over a finite field is a totally
disconnected, locally compact group, which may be thought of as
an "infinitedimensional Lie group". We study cocompact
lattices in such groups of rank 2, where the associated
building is a tree, using the group action on the tree and
finite group theory. This is joint work with Inna (Korchagina)
Capdeboscq.

April 14, 2010 
Tim Riley Cornell 
Hydra Groups
I will describe some wild geometry that arises in an apparently
benign group theoretic setting: I will exhibit a family of
groups enjoying a number of restrictive geometric and algebraic
conditions (they are CAT(0), biautomatic, 1relator, and
freebycyclic), and yet these groups have free subgroups of
huge (Ackermannian) distortion. The origin of this behaviour
lies in a simple computational game  a realisation of
Hercules' battle with the hydra, played out in manipulations of
strings of letters. This is work with Will Dison.

May 5, 2010 
Erika Meucci University of Utah 
Relative Outer Automorphisms of Free Groups
In this talk I will describe a (contractible) relative outer space on
which the group of relative outer automorphisms of a free group acts
properly and discontinuously.

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.