Low dimensional categories

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This project plans to study fundamental examples of higher categories in dimensions 2, 3, and 4, with the goal of understanding their essential features and building appropriate tools and theoretical frameworks for working with them. This work would have applications in several areas of mathematics including representation theory, low dimensional topology and topological quantum computing. Higher categories let us study the possible shapes of space (dimensions 2, 3, and 4, are the relevant ones for the world we live in), and also the dimensions in which we find the most interesting examples. The project plans to investigate particular examples related to exceptional Lie algebras, fusion categories, and categorical link invariants.