Group actions and symplectic techniques in Machine Learning and Computational Geometry

随着我们与世界的互动日益以数据为基础和相互联系，数学工具在广泛的科学学科中的相关性达到了前所未有的程度。拓扑学、几何学和统计学在计算机科学，特别是在数据科学中的地位日益上升，这一点尤其值得注意。数据是数字或基于数字的，因此通常带有潜在的拓扑、几何或统计结构。了解这种结构如何影响算法和感兴趣的属性将为算法开发带来立竿见影的好处，但这种创新需要计算机科学和数学方面的坚实基础。我的研究采取措施弥合这一差距，通过应用与以下相关的数学工具

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