MONDAY-------------

<br><br><span style="font-weight: bold;">9:40 - 10:40 Kai-Uwe Bux</span>: <span style="font-style: italic;">Finiteness Properties of the Braided Thompson Group  V_{br}.

 </span><br>(with Martin Fluch, Marco Schwandt, Stefan Witzel, and
 Matthew Zaremsky)

<br><br>Abstract. We prove that the braided Thompson group  V_{br}
is of type F_\infty.  We do this by constructing a suitable
space  X  on which  V_{br}  acts in such a way that we can
apply Brown's Criterion. The key step in verifying that  X
satisfies the conditions of Brown's Criterion is proving
higher connectivity properties of descending links with respect
to a height function.

To prove this, we inspect a subcomplex of the arc complex
of the plane with  n  marked points, where only those arc
systems are allowed whose arcs are pairwise disjoint.
This complex has the same connectivity as the matching
complex on a complete graph over  n  vertices.

<br><br><span style="font-weight: bold;">4:30 - 5:30 Tom Church:</span> <span style="font-style: italic;">A stability conjecture for the unstable cohomology of mapping
class groups, SL_n(Z), and Aut(F_n)

</span><br style="font-style: italic;"><br>Abstract: For each of the sequences of groups in the title, the i-th
rational cohomology is known to be independent of n in a linear range
n &gt;= Ci. Furthermore, this "stable cohomology" has been explicitly
computed in each case. In contrast, very little is known about the
unstable cohomology. In this talk I will explain a conjecture on a new
kind of stability in the cohomology of these groups. These conjectures
concern the unstable cohomology, in a range near the "top dimension".
One key ingredient is a version of Poincare duality for these groups
based on the topology of the curve complex and the algebra of modular
symbols. I'll finish by describing the evidence we have for these
conjectures, including some new vanishing theorems for the top
cohomology of M_g and of SL_n(Z). Joint work with Benson Farb and
Andrew Putman.

<br><br>TUESDAY-------------

<br><br><span style="font-weight: bold;">9:40 - 10:40 Thomas Koberda:</span> <span style="font-style: italic;">Canonical quasi-trees for right-angled Artin groups

</span><br><br>Abstract: Given a right-angled Artin group A, we associate to it a
canonical quasi-tree, called the extension graph.  We will discuss the
relationship between the structure of the quasi-tree and the structure
of right-angled Artin subgroups of A.  We will also discuss the
hyperbolic aspects of the action of A on its extension graph.  This
represents joint work with Sang-hyun Kim.


<br><br><span style="font-weight: bold;">4:30 - 5:30 Ken Bromberg:</span> <span style="font-style: italic;">Bounded cohomology with coefficients and groups acting on quasi-trees

</span><br><br>Abstract: This is joint work with M. Bestvina and K. Fujiwara. Using a
construction of Brooks we show that a free group has non-trivial
second bounded cohomology with coefficients in a uniformly convex
Banach space. The method extends to groups that act on a quasi-tree
with a free subgroup that acts with weak proper discontinuity. Using a
construction from earlier work with Bestvina and Fujiwara a large
class of groups have such actions including hyperbolic groups, CAT(0)
groups with rank one elements, mapping class groups and Out(F_n).

<br><br>WEDNESDAY-------------------


<br><br><span style="font-weight: bold;">9:40-10:40 Lee Mosher: </span><span style="font-style: italic;">Hyperbolicity of the free splitting complex of F_n</span> (joint
work with M. Handel)

<br><br>Abstract: The free splitting complex of F_n is a simplicial complex on
which Out(F_n) acts, also known as Hatcher's sphere complex and as the
simplicial completion of Culler and Vogtmann's outer space. We prove
that the free splitting complex, equipped with its simplicial metric,
is hyperbolic in the sense of Gromov.

<br><br>THURSDAY----------------

<br><br><span style="font-weight: bold;">9:40-10:40 Mark Feighn:</span> <span style="font-style: italic;">Subsurface projection in the Out(F_n)-setting

</span><br><br>Abstract: (joint with Mladen Bestvina) We present an analogue in the
Out(F_n)-setting of Masur and Minsky's subsurface projection.

<br><br><span style="font-weight: bold;">4:30-5:30 Ruth Charney:</span>  <span style="font-style: italic;">Outer Space for Right-Angled Artin Groups</span>

<br><br>Abstract: For any right-angled Artin group A, we build a contractible
space, analogous to the spine of outer space, on which a large
subgroup of Out(A) acts properly and cocompactly.  This is joint work
with K. Vogtmann and N. Stambaugh.  <br><br>FRIDAY-----------

<br><br><span style="font-weight: bold;">9:40-10:40 Doron Puder:</span> <span style="font-style: italic;">Measure preserving words are primitive.

</span><br><br>Abstract: We consider two properties of words in F_k, the free group
on k generators. A word w is called primitive if it belongs to a basis
(i.e. a free generating set) of F_k. It is called measure preserving
if for every finite group G, all elements of G are obtained by the
word map $w : G^k \to G$ the same number of times.

It is an easy observation that a primitive word is measure
preserving. Several mathematicians, most notably from Jerusalem, have
conjectured that the converse is also true. After proving the special
case of F_2, we manage to prove the conjecture in full in a joint work
with O. Parzanchevski. As an immediate corollary, we prove another
conjecture and show that the set of primitive words in F_k is closed
in the profinite topology.

Different tools are used in the proof, including Stallings core
graphs, random coverings of graphs, Mobius inversions and algebraic
extensions of free groups. The proof also involves a new algorithm to
detect primitive words and a new categorization of free words.