Survey of topological data analysis and applied topology

Survey of topological data analysis and applied topology

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Gunnar Carlsson, Stanford University
Fine Hall 214

There has been a great deal of work, both theoretical and applied, around the idea of approximating topology from discrete samples of geometric objects. The work in some instances involves direct interaction with the approximating complexes, and in others the use of analogues of homology. It has led to advances in data analysis, and also in other applications, such as sensor net technology. 

I will discuss these advances as well as future directions.