Actions of big mapping class groups on the arc graph- Carolyn Abbott (Columbia)
Abstract: Given a finite-type surface (i.e. one with finitely generated fundamental group), there are two important objects naturally associated to it: a group, called the mapping class group, and an infinite-diameter hyperbolic graph, called the curve graph. The mapping class group acts by isometries on the curve graph, and this action has been extremely useful in understanding the algebraic and geometric properties of mapping class groups. One particularly important class of elements of the mapping class group are those which act as loxodromic isometries of the curve graph; these are called “pseudo Anosov” elements. Given an infinite-type surface with an isolated puncture, one can associate two analogous objects: the big mapping class group and the (relative) arc graph. In this talk, we will consider the action of big mapping class groups on the arc graph, and, in particular, we will construct an infinite family of “infinite-type” elements that act as loxodromic isometries of the arc graph, where an infinite-type element is (roughly) one which is not supported on any finite-type subsurface. This is joint work with Nick Miller and Priyam Patel.
Morse Quasiflats- Jingyin Huang (Ohio State)
Abstract: We introduce the notion of Morse quasiflats, which is a common generalization of Morse quasigeodesics and quasiflats of top-rank. In the talk, we will provide motivations and examples for Morse quasiflats, as well as a number of equivalent definitions and quasi-isometric invariance (under mild assumptions). We will also show that Morse quasiflats are asymptotically conical, and provide several first applications. Based on joint work with B. Kleiner and S. Stadler.
Effective ping-pong in CAT(0) cube complexes- Kasia Jankiewicz (University of Chicago)
Abstract: Ping-pong lemma is a useful tool for finding elements in a given group that generate free semigroups. We use it to prove uniform exponential growth of certain groups acting on CAT(0) cube complexes. We also construct examples of groups with arbitrarily large gap between their cohomological and cubical dimensions. This is partially joint work with Radhika Gupta and Thomas Ng.
Mod p and torsion homology growth in nonpositive curvature- Kevin Schreve (University of Chicago)
Abstract: We compute the growth of mod p homology in finite index normal subgroups of right-angled Artin groups. We give examples where it differs from the rational homology growth, find such a group with exponential torsion growth, and for odd primes p construct closed locally CAT(0) manifolds with nontrivial mod p homology growth outside the middle dimension.