Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 18, 2014.

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events for the
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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 18, 2014

4:00 pm in 241 Altgeld Hall,Friday, April 18, 2014

#### Faces of Persistence

###### Ben Fulan (UIUC Math)

Abstract: Topological data analysis is a relatively new field that seeks to apply techniques from algebraic topology to problems that have traditionally been approached using statistical methods. One such problem is as follows: Given a set of points sampled randomly from a space $X$, can one recover the topological structure of $X$? A key technique that has been developed to address this question is persistent homology. We will give an introduction to this technique and compare different ways of presenting the resulting information, such as barcodes, persistence diagrams, and merge trees.

4:00 pm in 345 Altgeld Hall,Friday, April 18, 2014

#### Locally definable groups as covers of definable groups

###### Pantelis Eleftheriou (Universitaet Konstanz)

Abstract: A locally definable group in an o-minimal structure is a group whose domain is a countable union of definable sets $U_i$ and whose multiplication is definable when restricted to each $U_i \times U_j$. An important example is the universal cover of a definable group. We examine the following converse. Conjecture. Let $U$ be a connected abelian locally definable group which is generated by a definable set. Then $U$ is a cover of a definable group. In this talk we will report progress on the status of this conjecture and mention a number of statements that are equivalent to it. (Joint work with Y. Peterzil)