Sofía Martínez, Purdue University
2023 AWM Research Symposium
Pure and Applied Talks by Mathematicians Enhancing Diversity in Graduate Education (EDGE) [Organized by Quiyana M. Murphy and Sofía Martínez Alberga]

The latest methods of studying data involve the tools of topological data analysis (TDA). Even though the theoretical foundation of TDA comes from areas of math as abstract as algebraic topology, linear algebra, and homological algebra, the implementation of these tools can be done in a jupyter notebook with a few example packages. Given a data set, we use TDA to extrapolate information about the data set in particular its shape and we do this by looking at the highly persistent features that appear in its persistence diagram. For example, if we are given a time series we can determine if it is periodic or not if its image after preforming principal component analysis is dense in a circle. In this talk, we will discuss how using the structure of persistent cohomology can help distinguish two data sets that give rise to similar persistence diagrams.

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