On Thursday March 9th at 2 PM in Math Building 357, Ryan Jensen from the University of Tennessee will be talking about “Topological Data Analysis”.
Abstract: What is the shape of the following collection of data points (original image from Persistence Theory: From Quiver Representations to Data Analysis by Steve Y. Oudot)?
It depends on the “scale” from which the points are viewed. From a very small scale, all that is visible is a point; from a larger scale, there are multiple “B’s”; at an even larger scale, an “A” appears; finally, when viewed from a great distance, there is nothing but a blob.
In this talk we will give an introduction (accessible to undergraduates) to persistent homology, which is a tool from algebraic topology used to study the shape (homology) of data and through which scales that shape persists. We will look at the persistent homology of the above example as well as real life examples, including the shape of protein distribution in medicated cells. Finally, we will briefly discuss new results from large scale geometry which could be useful in determining other persistent properties of a data set.