# Search Research Symposium Abstracts

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## Stable commutator length on big mapping class groups

In this talk, we will discuss the stable commutator length function on the mapping class groups of infinite-type surfaces which satisfy a certain topological characterization. In particular, we will show that stable commutator length is a continuous function on these big mapping class groups, as well as that the commutator subgroups of these big mapping [Read More...]

**Presenter:**Elizabeth Field, University of Utah

**Authors:**Elizabeth Field, Priyam Patel, and Alexander Rasmussen

**Symposium Year:**2022

**Session:**Women in Groups, Geometry, and Dynamics

**Presentation Time:**June 17, 2022; 10:15 am

## Pants complexes for surfaces of infinite type

When S is an orientable surface of finite type, the pants complex is a fundamental tool for studying both the mapping class group and the Teichmuller space of S. When S is a surface of infinite type, there are several possible generalizations of the finite-type pants complex. We discuss some variations of infinite-type pants complexes, and we extend [Read More...]

**Presenter:**Beth Claire Branman, University of Virginia

**Authors:**Beth Claire Branman

**Symposium Year:**2022

**Session:**Women in Groups, Geometry, and Dynamics

**Presentation Time:**June 17, 2022; 10:40 am

## Uniqueness of Equilibrium States for Geodesic Flow on Translation Surfaces

Some translation surfaces are examples of compact surfaces of genus ≥2 equipped with a metric that is flat everywhere except at finitely many cone points that have angle greater than 2π. When possible, we avoid geodesics that avoid cone points (the singular set) and use the hyperbolicity introduced by the cone points. We show that that sufficiently [Read More...]

**Presenter:**Noelle Sawyer, Southwestern University

**Authors:**Benjamin Call, David Constantine, Alena Erchenko, Noelle Sawyer, and Grace Work

**Symposium Year:**2022

**Session:**Women in Groups, Geometry, and Dynamics

**Presentation Time:**June 17, 2022; 11:05 am

## The Shrinking Target Problem in the Context of Moduli Spaces of Translation Surfaces

Consider a nested family of targets shrinking at a specified rate and a given flow, we want to understand the set of points that hit these targets infinitely often under the flow. One way to examine this set is to determine under what conditions this set has full measure. This question is closely related to the Borel Cantilli lemma and also gives rise to [Read More...]

**Presenter:**Grace Work, University of Wisconsin-Madison

**Authors:**Spencer Dowdall, Grace Work

**Symposium Year:**2022

**Session:**Women in Groups, Geometry, and Dynamics

**Presentation Time:**June 17, 2022; 11:30 am

## Random Groups Acting on CAT(0) Cube Complexes

Random groups are one way to study "typical" behavior of groups. In the Gromov density model, we often find a threshold density above which a property is satisfied with probability 1, and below which it is satisfied with probability 0. Two properties of random groups that have been well studied are cubulation (or more generally, acting cocompactly on a [Read More...]

**Presenter:**MurphyKate Montee, Carleton College

**Symposium Year:**2022

**Session:**Women in Groups, Geometry, and Dynamics

**Presentation Time:**June 17, 2022; 3:30 pm

## Topological and dynamical methods in studying orderable 3-manifold groups

A nontrivial group is called left-orderable if it admits a left-invariant order. In this talk, we will first survey the background, open questions, and conjectures related to the orderability of 3-manifold groups. Then we will discuss how this seemingly pure algebraic problem is naturally tied to the manifolds' dynamics and [Read More...]

**Presenter:**Ying Hu, University of Nebraska Omaha

**Symposium Year:**2022

**Session:**Women in Groups, Geometry, and Dynamics

**Presentation Time:**June 17, 2022; 3:55 pm

## The Lens Space Recognition Problem and Seifert Fiber Spaces

The Lens Space Recognition Problem is the problem of deciding whether a given 3-manifold is a lens space (including S^3). A decision problem is said to lie in NP if an affirmative solution can be verified via certificate in polynomial time relative to the input size (of a triangulation in this case) and we say that a problem lies in coNP if a negative [Read More...]

**Presenter:**Kate Petersen, University of Minnesota Duluth

**Authors:**Neil Hoffman and Kate Petersen

**Symposium Year:**2022

**Session:**Women in Groups, Geometry, and Dynamics

**Presentation Time:**June 17, 2022; 4:20 pm

## Totally geodesic surfaces in knot complements with small crossing number

Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader-Fisher-Miller-Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite [Read More...]

**Presenter:**Rebekah Palmer, Temple University

**Symposium Year:**2022

**Session:**Women in Groups, Geometry, and Dynamics

**Presentation Time:**June 17, 2022; 4:45 pm

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