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An Overview of Persistent Homotopy

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Dr. David Letscher

What
  • Computer Science Seminar
When Mon, Sep 26, 2016
from 03:10 PM to 04:00 PM
Where Ritter Hall 115
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Since it's development in 1999, persistent homology has become a foundational technique in the field of computational topology. In particular, it has become a very useful tool for identifying topological features in unstructured data and has been applied to a broad range of application domains. Persistent homotopy, though defined at the same time, has been less studied. This is for two primary reasons: persistent homology can be computed efficiently and is easily interpreted. In the first part of this talk we will develop the theory of persistent homotopy and will introduce a framework for its interpretatin. In the second part of the talk, we will discuss the problem of removing topological noise from a dataset. In two dimensions, persistent homology can be used efficiently to remove topological noise of any particular scale. However; in three dimension this is not possible using homological techniques. Borrowing techniques from 3-manifold topology, we will show how persistent homotopy can be used to remove topological noise. If time permits, we will discuss how the topological denoise problem is intractable in higher dimensions.
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