Department of

Mathematics


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

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Friday, September 23, 2016

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

Analysis and Topology: A Tale of Two Indices

Hadrian Quan (UIUC Math)

Abstract: The Atiyah-Singer Index Theorem provides a link between algebraic topology, differential geometry, partial differential equations, operator algebras, and physics. In its simplest statement, it asserts that two numbers: an integer and a rational, which are computed in two remarkably different manners are in fact the same number. In this talk we’ll unpack a few of the many ideas that went into this theorem and its various proofs.

4:00 pm in 345 Altgeld Hall,Friday, September 23, 2016

Extending partial isometries

Mahmood Etedadi Aliabadi (UIUC Math)

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.