Geometry colloquium October 4, 2010

The speaker is Afra Zomorodian of the Dartmouth College Computer Science Department, who will speak on

Topological Data Analysis

ABSTRACT: Scientific data is often in the form of a finite set of sampledpoints. Analysis assumes that this data has structure: It is sampled fromsome underlying geometric space. Topological data analysis focuses on re-covering this space’s topology: how it is connected.We generally follow a two-step process in topological analysis. In the firststep, we approximate the space in a combinatorial structure. In the secondstep, we capture its topology using an algebraic invariant.In this talk, I discuss the theory and practice of topological data analysiswith a focus on tidy simplicial sets for step 1 and theories of persistence forstep 2. I will also include some applications to real-world data.

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