Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, September 11, 2019.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, September 11, 2019

3:00 pm in 241 Altgeld Hall,Wednesday, September 11, 2019

#### On spatial actions and whirly actions

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

Abstract: Given a Borel measure-preserving action of a Polish group $G$ on $\left[ 0,1 \right]$, ignoring null sets gives a corresponding action on the measure algebra. If $G$ is locally compact, this can always be reversed: a measure-preserving action on the measure algebra of $\left[ 0,1 \right]$ can always be induced by a (pointwise) action on $\left[ 0,1 \right]$. This fails in the non-locally-compact case. In this talk, I will discuss a dynamical condition on the action ("whirliness") which characterizes when an action on the measure algebra admits a pointwise realization. This talk is based on 'Spatial and non-spatial actions of Polish groups' by E Glasner and B Weiss.

4:00 pm in 245 Altgeld Hall,Wednesday, September 11, 2019

#### Trees and leaves where boundaries meet

###### Elizabeth Field   [email] (Illinois Math)

Abstract: If $H$ and $G$ are hyperbolic groups with $H\leq G$, one can ask if the inclusion map from $H$ into $G$ extends continuously to a map from the boundary of $H$ into the boundary of $G$. If such a map exists, we call this map the Cannon-Thurston map. In this talk, we will first draw inspiration from the setting originally studied by Cannon and Thurston which has a particularly nice geometry. We will then take a brief tour through the world of geometric group theory, where we will discuss the notion of a hyperbolic group and its boundary. Finally, we will return to explore various geometric, topological, and algebraic properties of the Cannon-Thurston map.

4:00 pm in 447 Altgeld Hall,Wednesday, September 11, 2019

#### Compactified Jacobian

###### Lutian Zhao (Illinois Math)

Abstract: In this talk, I will start by a brief review of the history of Jacobians. Then I will describe the definition of compactified Jacobian as they are crucial object in studying singular curves. The final goal is to understand a calculation on the compactified Jacobian of the curve $x^p-y^q=0$ for $p,q$ coprime, where the Euler characteristic of the Compactified Jacobian is exactly the Catalan number $C_{p,q}$.