9:40 - 10:40 Kai-Uwe Bux: Finiteness Properties of the Braided Thompson Group V_{br}.

(with Martin Fluch, Marco Schwandt, Stefan Witzel, and Matthew Zaremsky)

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.

4:30 - 5:30 Tom Church: A stability conjecture for the unstable cohomology of mapping class groups, SL_n(Z), and Aut(F_n)

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 >= 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.

TUESDAY-------------

9:40 - 10:40 Thomas Koberda: Canonical quasi-trees for right-angled Artin groups

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.

4:30 - 5:30 Ken Bromberg: Bounded cohomology with coefficients and groups acting on quasi-trees

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).

WEDNESDAY-------------------

9:40-10:40 Lee Mosher: Hyperbolicity of the free splitting complex of F_n (joint work with M. Handel)

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.

THURSDAY----------------

9:40-10:40 Mark Feighn: Subsurface projection in the Out(F_n)-setting

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

4:30-5:30 Ruth Charney: Outer Space for Right-Angled Artin Groups

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.

FRIDAY-----------

9:40-10:40 Doron Puder: Measure preserving words are primitive.

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.