Abstract: This talk is an introduction to applied and computational topology. The shape of a dataset often reflects important patterns within. Two such datasets with interesting shapes are a space of 3x3 pixel patches from optical images, which can be well-modeled by a Klein bottle, and the configuration space of the cyclo-octane molecule, which is a Klein bottle glued to a 2-sphere along two circles. I will introduce topological tools (such as persistent homology) for visualizing, understanding, and performing machine learning tasks on high-dimensional datasets.

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Comunicaciones DCC