By work of Goodwillie-Weiss, given any manifold $M$ with boundary, there is a cosimplicial space whose totalization is a close approximation to the space of embedding of $[0,1]$ in $M$ with fixed behaviour at the boundary. The resulting homology spectral sequence is known to collapse rationally for $M=\mathbb{R}^n$ by work of Lambrechts-Turchin and Volic. I will explain a new proof of this result which can be generalized to a manifold of the form $M=X\times[0,1]$ with $X$ a smooth and proper complex algebraic variety. This involves constructing an action of some Galois group on the completion of the cosimplicial space. This is joint work with Pedro Boavida de Brito and Danica Kosanovic.

Quotients are a powerful tool used for constructing exotic embeddings in groups that act on negatively curved metric spaces.  Models for random quotients originate in work of Gromov, Arzhantseva and Ol’shanskii where relations are sampled from spheres in free groups to study genericity of properties like hyperbolicity.  I will introduce a new model for random quotients of groups that instead samples relations using random walks and describe how this model is well-adapted to studying quotients of groups with more flexible actions on hyperbolic spaces and discuss geometric tools used to establish when these more general forms of negative curvature are preserved in random quotients. These techniques also provide new examples of groups that are quasi-isometrically rigid and exotic common quotients.  This talk will be based on joint work with Abbott, Berlyne, Mangioni, and Rasmussen.

I will report on work joint with Florian Naef in which we produce, for a map f of spaces over a space B such that f has compact fibers, a rational model for the fiberwise transfer of fiberwise topological Hochschild homology, considered as a map of parametrized spectra over B. This is motivated by applications to moduli spaces of manifolds: in particular we can detect the vanishing of certain cohomology classes originating from a graph complex via the classifying space of homotopy automorphisms.
 

In this talk we will discuss the connection between combinatorial properties of minimally self-intersecting curves on a surface S and the geometric behaviour of geodesics on S when S is endowed with a Riemannian metric. In particular, we will explain the interplay between a smoothing, which is a type of surgery on a curve that resolves a self-intersection, and k-systoles, which are shortest geodesics having at least k self-intersections, and we will present some results that partially elucidate this interplay. There will be lots of pictures. Based on joint work with Max Neumann-Coto.

Introduced by Bestvina and Brady in 1997, Bestvina—Brady groups form an important class of examples in geometric group theory and topology, known for exhibiting unusual finiteness properties. In this talk, I will focus on the Dehn functions of finitely presented Bestvina—Brady groups. Very roughly speaking, the Dehn function of a group measures how difficult it is to fill loops by discs in spaces associated to the group, and captures geometric information that is invariant under coarse equivalence. After reviewing known results, I will present a classification of the Dehn functions of Bestvina—Brady groups. This talk is based on joint work with Yu-Chan Chang and Matteo Migliorini.

As temperatures are increasing, so is the presence of meltwater lakes sitting on the surface of the Greenland Ice Sheet. Such lakes have the possibility of draining through cracks in the ice to the bedrock. Observed discharge rates have found that these lakes can drain at three times the flow rate of Niagara Falls. Current models of subglacial drainage systems are unable to cope with such a large and sudden volume of water. This motivates the idea of a 'subglacial blister' which propagates and slowly dissipates underneath the ice sheet. We present a basic hydrofracture model for understanding this process, before carrying out a number of extensions to observe the effects of turbulence, topography, leak-off and finite ice thickness.