Algebraic Topology and Geometric Pattern Recognition

With the "blizzard" of data being generated by scientists in all disciplines, the development of tools for analyzing it has become a very high priority task. In particular, methods for quick qualitative analysis are of particular value. In this talk, I will describe one such method, based on the mathematical formalism called homology theory. I will discuss the mathematical background, how it is modified to be able to deal with situations where there is noise and where one has incomplete information, and finally illustrate with some examples.