Today I gave a twenty-minute talk at UI Chicago as part of the first annual Chicago Area Student SIAM Conference. My talk was titled “Recent Developments in Persistent Homology,” and it foreshadows the theoretical foundations and computational implementations we’ll be laying out on this blog in the coming months. Here’s the abstract:

Persistent homology is a recently developed technique for analyzing the topology of data sets. We will give a rough overview of the technique and sample successful applications to areas such as natural image analysis & texture classification, breast and liver cancer classification, molecular dynamical systems, and others.

The talk was received very well — mostly, I believe, because I waved my hands on the theoretical aspects and spent most of my time talking about the applications.

In any case, although the slides I used for my talk were largely unannotated (I spoke much more than is contained in text on the slides), I did list a number of references to papers that have shown successful applications. As such, some of the audience members asked me to post the slides on the web.

I personally hate it when people post slides because they’re often taken out of context (or just slide after slide of dense text), so this is just a warning to the reader. If you didn’t attend my talk, the chances are you won’t get much out of these slides. If you did, I hope the slides will be useful for the references and to jog your memory about my talk.