Group actions and symplectic techniques in Machine Learning and Computational Geometry

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Mathematical tools have become relevant across a broad range of scientific disciplines to an extent never before seen, as our interactions with the world become increasingly data-based and inter-connected. The rising role of topology, geometry and statistics in Computer Science, especially in Data Science, is particularly noticeable. Data are numbers or number-based and so often come with underlying topological, geometric or statistical structure. Understanding how this structure impacts algorithms and properties of interest confers an immediate benefit to algorithmic development, but this innovation requires solid foundations in both Computer Science and Mathematics. My research takes steps to bridge this gap, by applying mathematical tools related to