Carolyn Abbott (April 7-9, 2026)

Carolyn Abbott is an Assistant Professor at Brandeis University and the Landsman Career Development Chair in the Sciences. Her research focuses on geometric group theory, the study of groups through their actions on metric spaces. She is particularly interested in groups that act by isometries on hyperbolic metric spaces.  Research focuses include big mapping class groups, acylindrically hyperbolic groups, hierarchically hyperbolic groups and spaces, and other actions of groups on hyperbolic spaces.

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Transportation on Thursday, April 19 will be available between Northfield and Minneapolis in the form of van(s).  If you would like to ride in one of the vans, please use this form to sign up. Registration is not necessary, but in the case that there are more people than space we will prioritize those who have registered.

Abstracts

Introductory Talk: When Surfaces Stretch and Twist: Understanding Mapping Classes
Abstract: Surfaces, like the sphere, the torus (a donut), or more complicated shapes with multiple “holes,” are fundamental objects in topology. One way to study a surface is to look at its symmetries: all the ways you can stretch or deform the surface continuously without tearing or gluing. The collection of these symmetries forms the mapping class group. A remarkable result, called the Nielsen–Thurston classification, says that for sur- faces of finite type, every such symmetry falls into one of three types: periodic (repeating after some number of steps), reducible (preserving some simpler structure on the surface), or pseudo-Anosov (exhibiting a kind of “chaotic” stretching behavior). In this talk, we will introduce these ideas through concrete examples and build intuition for how these different behaviors arise.

We will then turn to the much less understood world of infinite-type surfaces, whose topology is dramatically more complicated. Many classical tools break down in this setting, and the Nielsen–Thurston classification no longer holds in its original form. We will give a taste of what goes wrong and highlight new phenomena that arise. The goal is to give a glimpse of how a well-understood theory evolves and becomes richer when one moves beyond the finite-type setting.

Colloquium Talk: Hyperbolic Actions of Big Mapping Class Groups 
Abstract: Mapping class groups, that is, symmetries of surfaces up to deformation, admit natural actions on Gromov hyperbolic spaces, most prominently via the curve complex. For finite-type surfaces, the celebrated Nielsen–Thurston classification is partially reflected in this action, with pseudo-Anosov elements acting as loxodromic isometries.

For infinite-type surfaces, this picture becomes more subtle. I will describe hyperbolic graphs adapted to this setting and focus on constructing loxodromic elements and studying their limit sets, which encode geometric and topological information about the dynamics of their action on the surface. These developments highlight both the challenges and new phenomena that arise in the large-scale geometry of big mapping class groups. This is joint work with N. Miller, P. Patel, A. Vadnere, and P. Pham.

Livestreaming: TBD