Schedule


Preconference Talks 
Thursday, April 16


3:10  4:00 PM 4088 East Hall 

Thomas Koberda 

Homological Representation Theory of The Mapping Class
Group I seek to understand the algebraic structure of the mapping class
group and the dynamical behavior of
individual classes by studying the representation theory of the
mapping class group on the homology of
certain finite covers. I will explain how we can construct a faithful
infinitedimensional representation of
the mapping class group and recover the NielsenThurston
classification of each class. I will also indicate
connections with the representation theory of nilpotent Lie groups.


4:10  5:00 PM 1360 East Hall 

Benson Farb 

Surface bundles over surfaces
The goal of this talk will be to survey the theory of
surface bundles over surfaces. This topic connects to areas
from algebraic geometry to combinatorial group theory to
Teichmuller theory. This largely unexplored subject has many
open questions, some of which will be presented in this talk.


RTG WORKSHOP ON GEOMETRIC GROUP THEORY 
Friday, April 17 
B844 East Hall 

1:30  2:30 PM 

Mladen Bestvina 

Prehistory
Nielsen, Magnus, Whitehead. Stallings'
folds. Finite generation of Out(F_n) and related algorithms


2:45  3:45 PM 

KaiUwe Bux 

Symmetric spaces, Siegel domains and consequences.
Definition of arithmetic groups, elementary properties;
the geometries associated to arithmetic groups and
Siegel domains. SL_n(Z) will be the running example.


4:15  5:15 PM 

Benson Farb 

Algebraic Structure
Dehn twists, finite generation, the lantern and H_1, presentations,the symplectic representation, virtual torsionfreeness 






Saturday,
April 18  B844 East Hall 

9:00  10:00 AM 

Benson Farb


The NielsenThurston Classification and pseudoAnosov theory
Construction of pseudoAnosovs, the main theorem, analogy with SL(2,Z), Thurston proof, Bers proof


10:30  11:00 AM 

ChiaYen Tsai 

Asymptotics of least pseudoAnosov
dilatations The mapping class group of S is the
set of all surface homeomorphisms of S up to isotopy. The
NielsenThurston classification says that a mapping class is
either periodic, reducible, or pseudoAnosov. Each pseudoAnosov
mapping class is equipped with a real number >1 called the
dilatation. We will consider the least dilatation for each
surface. In this talk, we will discuss the asymptotic behavior
of least pseudoAnosov dilatations when we vary genus and the
number of marked points of a surface. 

11:15  11:45 AM 

Johanna Mangahas 

Uniform uniform exponential growth of subgroups of the
mapping class group Like linear groups and hyperbolic
groups, subgroups of the mapping class group with exponential
growth have uniform exponential growth; furthermore, their
minimal growth rates have a lower bound which depends on the
surface, and not the particular subgroup. I'll describe the
proof, and also show why any lower bound necessarily depends on
the topological type of the surface. 

1:15  2:15 PM 

KaiUwe Bux 

Homological properties and duality Further
exploiting the action on symmetric spaces; homological
properties in particular BieriEckmann duality


2:30  3:00 PM 

Tom Church 

Orbits of curves under the
Torelli group and the Johnson kernel It is not difficult to determine when two collections of
curves are in the same orbit under the mapping class group; the
solution relies just on the classification of surfaces. A major
advance came in work of Dennis Johnson, who gave a simple but powerful
argument to describe the orbit of a bounding pair or separating curve
under the action of the Torelli group. We will describe the proof of
Johnson's theorem and explain how to extend the result to arbitrary
collections of curves. Finally, we will outline a new perspective on
the Johnson homomorphism that allows us to characterize orbits of
curves under the Johnson kernel. 

3:15  3:45 PM 

Jing Tao 

Linearly Bounded Conjugator Property for the Mapping Class Group
Given two conjugate mapping classes f and g, we produce a
conjugating element w such that w ≤ K (f + g), where  · 
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. 

4:15  5:15 PM 

Mladen Bestvina 

Topology of Out(F_n)
Definition
of outer space, spine, finiteness properties. Proof of homology
stability. Traintracks. 

6:00 PM 

Banquet 

Middle Kingdom
332 S Main St
(734) 6686638
Ann Arbor, MI 48104 

Sunday, April 19 
B844 East Hall 

9:15  10:15 AM 

Mladen Bestvina


Geometry of Outer space.
Proof of existence of traintracks for irreducible autos a la Bers. Where do we stand? 

10:45  11:45 AM 

KaiUwe Bux 

Generalizations of arithmetic groups
Sarithmetic groups and arithmetic groups in positive
characteristic and the associated geometries


12:00  1:00 PM 

Benson Farb 

Comparisons between mapping class groups and arithmetic groups
Analogies, similarities, differences ((co)homological, algebraic, geometric).







