Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 27, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 27, 2018

4:00 pm in 241 Altgeld Hall,Friday, April 27, 2018

#### Cannon-Thurston Maps

###### Elizabeth Field (UIUC)

Abstract: When a map between two objects extends to a continuous map between their boundaries, this boundary map is called the Cannon-Thurston map. When the objects at play are a hyperbolic group and a hyperbolic subgroup, there are two main questions which arise from this definition. First, when does the Cannon-Thurston map exist? Further, if such a map exists, can the fibers of this map be described in some nice algebraic or geometric way? In this talk, we will introduce the background needed to understand these questions. We will then briefly explore some of what is known about their answers, as well as some open questions which remain.