Wrinkles on Everest: Persistence and Stability in an Omniscalar World

Dmitriy Morozov, Lawrence Berkeley National Laboratory
September 11th, 2013 at 3:30PM–4:30PM in 939 Evans Hall [Map]

In the last decade, persistent homology emerged as a particularly active topic within the young field of computational topology. Homology is a topological invariant that counts the number of cycles in the space: components, loops, voids, and their higher-dimensional analogs. Persistence keeps track of the evolution of such cycles and quantifies their longevity. By encoding physical phenomena as real-valued functions, one can use persistence to identify their significant features.

This talk is an introduction to the subject, discussing the settings in which persistence is effective as well as the methods it employs. It will touch on the topics of homology inference, dimensionality reduction, and general models of noise. The last part of the talk will describe our recent efforts to parallelize computation of merge trees, a descriptor closely related to 0-dimensional persistence.