Department of

# Mathematics

Seminar Calendar
for events the day of Friday, September 23, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2016           September 2016          October 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6                1  2  3                      1
7  8  9 10 11 12 13    4  5  6  7  8  9 10    2  3  4  5  6  7  8
14 15 16 17 18 19 20   11 12 13 14 15 16 17    9 10 11 12 13 14 15
21 22 23 24 25 26 27   18 19 20 21 22 23 24   16 17 18 19 20 21 22
28 29 30 31            25 26 27 28 29 30      23 24 25 26 27 28 29
30 31


Friday, September 23, 2016

4:00 pm in 241 Altgeld Hall,Friday, September 23, 2016

#### Analysis and Topology: A Tale of Two Indices

Abstract: It is known that if a group $G$ acts on a metric space $X$ then the question of whether there is a finitely additive $G$-invariant measure on Borel subsets of $X$ is equivalent to some geometric condition on $X$. Therefore, it is of interest whether we can extend partial isometries of $X$ into a group, e.g., can we extend a compact $X$ into another compact metric space such that each partial isometry of $X$ extends to a full isometry of $Y$. We talk about some results in the case where $X$ is finite. Also, we show that for a compact $X$ and $\epsilon>0$ it is possible to find a compact metric space $Y$, such that $Y$ extends $X$ and every partial isometry of $X$ extends to a full isometry of $Y$ with $\epsilon$ distortion.