# Geometry and Topology Seminar

Current contact: Dave Futer or Matthew Stover

The Seminar usually takes place on Wednesdays at 2:30 PM in Room 617 on the sixth floor of Wachman Hall.

• Wednesday January 25, 2017 at 14:30, Wachman 617
Divergence of CAT(0) cube complexes and right-angled Coxeter groups

Ivan Levcovitz, CUNY Graduate Center

Abstract: The divergence function of a metric space, a quasi-isometry invariant, roughly measures the rate that pairs of geodesic rays stray apart. We will present new results regarding divergence functions of CAT(0) cube complexes. Right-angled Coxeter groups, in particular, exhibit a rich spectrum of possible divergence functions, and we will give special focus to applications of our results to these groups. Applications to the theory of random right-angled Coxeter groups will also be briefly discussed.

• Wednesday February 1, 2017 at 14:30, Wachman 617
Universal acylindrical actions

Carolyn Abbott, University of Wisconsin

Abstract: Given a finitely generated group, one can look for an acylindrical action on a hyperbolic space in which all elements that are loxodromic for some acylindrical action of the group are loxodromic for this particular action. Such an action is called a universal acylindrical action and, for acylindrically hyperbolic groups, tends to give a lot of information about the group. I will discuss recent results in the search for universal acylindrical actions, describing a class of groups for which it is always possible to construct such an action as well as an example of a group for which no such action exists.

• Thursday February 9, 2017 at 16:30, David Rittenhouse Labs, UPenn
Stability and vanishing in the unstable cohomology of SL_n(Z)

Thomas Church, Stanford/IAS

PATCH seminar (organized by Bryn Mawr, Haverford, Penn, and Temple)

Abstract: Borel proved that in low dimensions, the cohomology of a locally symmetric space can be represented not just by harmonic forms but by invariant forms. This implies that the $k$-th rational cohomology of $SL_n(Z)$ is independent of $n$ in a linear range $n \geq c k$, and tells us exactly what this "stable cohomology" is. In contrast, very little is known about the unstable cohomology, in higher dimensions outside this range.

In this talk I will explain a conjecture on a new kind of stability in the unstable cohomology of arithmetic groups like $SL_n(Z)$. These conjectures deal with the "codimension-k" cohomology near the top dimension (the virtual cohomological dimension), and for $SL_n(Z)$ they imply the cohomology vanishes there. Although the full conjecture is still open, I will explain how we proved it for codimension-0 and codimension-1. The key ingredient is a version of Poincare duality for these groups based on the algebra of modular symbols, and a new presentation for modular symbols. Joint work with Benson Farb and Andrew Putman.

• Thursday February 9, 2017 at 17:45, David Rittenhouse Labs, UPenn
Lagrangian tori, mutations and toric degenerations

Denis Auroux, UC Berkeley/IAS

PATCH seminar (organized by Bryn Mawr, Haverford, Penn, and Temple)

Abstract: A basic open problem in symplectic topology is to classify Lagrangian submanifolds (up to, say, Hamiltonian isotopy) in a given symplectic manifold. In recent years, ideas from mirror symmetry have led to the realization that even the simplest symplectic manifolds (eg. vector spaces or complex projective spaces) contain many more Lagrangian tori than previously thought. We will present some of the recent developments on this problem, and discuss some of the connections (established and conjectural) between Lagrangian tori, cluster mutations, and toric degenerations, that arise out of this story.

• Wednesday February 15, 2017 at 14:30, Wachman 617
Experimental statistics of veering triangulations

William Worden, Temple University

Abstract: Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. We present experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. We will begin by discussing essential background material, including hyperbolic manifolds and ideal triangulations, and more particularly fibered hyperbolic manifolds and the construction of the veering triangulation.

• Wednesday February 22, 2017 at 14:30, Wachman 617
Minimal surfaces with bounded index

Davi Maximo, University of Pennsylvania

Abstract: In this talk we will give a precise picture on how a sequence of minimal surfaces with bounded index might degenerate on a given closed three-manifold. As an application, we prove several compactness results.

• Wednesday March 1, 2017 at 14:30, Wachman 617
TBA

William Goldman, University of Maryland

• Friday March 3, 2017 at 14:30, Wachman 617
TBA

Sara Maloni, University of Virginia

PATCH seminar (organized by Bryn Mawr, Haverford, Penn, and Temple)

• Friday March 3, 2017 at 16:00, Wachman 617
TBA

Laura Starkson, Stanford University

PATCH seminar (organized by Bryn Mawr, Haverford, Penn, and Temple)

• Wednesday April 5, 2017 at 14:30, Wachman 617
TBA

Michael Magee, Yale University

TBA