Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 26, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 26, 2019

4:00 pm in 345 Altgeld Hall ,Friday, April 26, 2019

#### On generic monothetic subgroups of Polish groups

###### Dakota Ihli (UIUC Math)

Abstract: Given a Polish group $G$, what can be said about the subgroup $\overline{\left\langle g \right\rangle}$ for the generic element $g \in G$? In this talk we will discuss progress and open problems in this area. Special emphasis will be given on the group of measure-preserving automorphisms of the unit interval.

4:00 pm in 145 Altgeld Hall,Friday, April 26, 2019

#### Relatively hyperbolic groups and Dehn fillings

###### Heejoung Kim (UIUC)

Abstract: Geometric group theory has been studied extensively since Gromov introduced the notion of a hyperbolic group. For instance, the fundamental group of a hyperbolic surface is a hyperbolic group, but not the fundamental group of a cusped hyperbolic 3-manifold. From this motivating example, we consider a generalization of a hyperbolic group, called a relatively hyperbolic group. On the other hand, Thurston's Dehn filling theorem states that one can obtain further hyperbolic 3-manifolds from a given cusped hyperbolic 3-manifold. Groves and Manning extended Thurston's Dehn filling theorem to the context of relatively hyperbolic groups. In this talk, we will discuss hyperbolic groups, relatively hyperbolic groups, and the group-theoretic analog of Thurston's Dehn filling theorem in the context of relatively hyperbolic groups.