Andrey Gogolev - Anosov bundles

Consider a non-trivial fiber bundle M -> E -> B whose total space E is compact and whose base B is simply connected. Can one equip E with a diffeomorphism or a flow which preserves each fiber and whose restriction to each fiber is Anosov? In a joint work with Tom Farrell we answer this question negatively and give an application to geometry of negatively curved bundles. However, in a joint work with Pedro Ontaneda and Federico Rodriguez Hertz, we construct non-trivial bundles that admit fiberwise Anosov diffeomorphisms that permute the fibers.

Kate Juschenko - Extensions of amenable groups by recurrent groupoids

I will discuss a theorem on amenability which unifies many know technical proofs of amenability to the one common proof as well as produces examples of groups for which amenability was an open problem. This is joint with V. Nekrashevych and M. de la Salle.

Sang-hyun Kim - A curve complex for a right-angled Artin group

Each right-angled Artin group (RAAG, in short) G canonically acts on a quasi-tree T, which we call as the extension graph of G. We survey combinatorial, algebraic and geometric aspects of this quasi-tree, in an analogous manner to the curve complex of a surface. One of the corollaries is that, every RAAG contained in a mapping class group embeds into another RAAG generated by powers of Dehn twists (Joint work with Thomas Koberda).

Alexander Kolpakov - Hyperbolic manifolds with one cusp

I shall introduce a simple algorithm which transforms every four-dimensional cubulation into a cusped finite-volume hyperbolic four-manifold. Combinatorially distinct cubulations give rise to topologically distinct manifolds. The algorithm produces the first examples of finite-volume hyperbolic four-manifolds with one cusp. More generally, the number of k-cusped hyperbolic four-manifolds with volume smaller than V grows like C^{V log V} for any fixed k. As a corollary, I deduce that the 3-torus bounds geometrically a hyperbolic manifold. This is a joint work with Bruno Martelli (University of Pisa, Italy).

Jason Manning - A new proof of Wise's malnormal special quotient theorem

Wise's malnormal special quotient theorem (MSQT) is a key ingredient in the recent resolution by Agol of some central conjectures in 3-manifolds, including the virtual Haken conjecture. The MSQT allows one to perform certain small-cancellation operations or "Dehn fillings" on a virtually special hyperbolic group, in such a way that the result is still hyperbolic and virtually special. I'll try to give an idea how this theorem is used and outline a new proof by Agol, Groves, and myself.

Sam Taylor - Subfactor projections and fully irreducible automorphisms of free groups

Much of the progress made on understanding the geometry of the mapping class group over the last 15 years has used Masur-Minsky subsurface projection as a central tool. Recently, Bestvina and Feighn introduced subfactor projections as an analogous tool to study Out(Fn). In this talk, I'll introduce the basic properties of subfactor projections and, as an application, give a construction of fully irreducible automorphisms of free groups. I'll conclude by describing a few potential applications of subfactor projections to open problems.