Stable commutator length in graphs of groups- Lvzhou (Joe) Chen (University of Chicago)
Abstract: The stable commutator length (scl) is a relative version of the Gromov-Thurston norm. For a given null-homologous loop L in a space X, its scl is the infimal complexity of surfaces bounding L, measured in terms of Euler characteristics. Surfaces realizing the minimal complexity are called extremal. They are pi_1-injective, and can only exist when scl is rational. We show that scl takes rational values for all loops in a space X if pi_1(X) is certain graphs of groups, inclusing Baumslag-Solitar groups. Moreover, there is a linear programming algorithm to compute scl.
Flows, Thurston norm, and surfaces: homology to isotopy- Michael Landry (Washington University)
Abstract: Let M be a closed hyperbolic 3-manifold. We begin by reviewing a classical picture due to Thurston, Fried, and Mosher in which a single pseudo-Anosov flow organizes the data of a fibered face F of the Thurston norm ball of M as well as certain nice surface representatives of homology classes lying in the cone over F. We then announce a new theorem which strengthens the above by collating all isotopy classes of incompressible surfaces representing classes in the cone over F. We explain that the result follows from a more general theorem, involving veering triangulations, which also applies to other faces of the Thurston norm ball (possibly nonfibered, possibly lower-dimensional).
Dehn filling and knot complements that irregularly cover- William Worden (Rice University)
Abstract: It is a longstanding conjecture of Neumann and Reid that exactly three knot complements can irregularly cover a hyperbolic orbifold---the figure-8 knot and the two Aitchison--Rubinstein dodecahedral knots. This conjecture, when combined with work of Boileau--Boyer--Walsh, implies a more recent conjecture of Reid and Walsh, which states that there are at most 3 knot complements in the commensurability class of any hyperbolic knot. We give a Dehn filling criterion that is useful for producing large families of knot complements that satisfy both conjectures. The work we will discuss is partially joint with Hoffman and Millichap, and partially joint with Chesebro, Deblois, Hoffman, Millichap, and Mondal.