We investigate deep structural connections unifying number theory, algebra, and representation theory with string and quantum field theories. The Moonshine phenomenon bridges the number-theoretic world of modular objects with the representation theory of finite groups and vertex operator algebras, while relating to geometry and string theory. We also apply similar tools to low-dimensional topology, proposing a new avenue that relates the physical, algebraic, and analytic structures of novel topological invariants.
We explore the two-way exchange between theoretical physics and machine learning. On one side, we use generative AI to solve hard physics problems, such as assisting simulations of lattice field theory. In the other direction, we treat neural networks as physical systems. By applying principles like thermodynamics and renormalization group flows, we aim to interpret how deep learning works and design smarter, more efficient architectures.
We explore how AI can augment research in pure mathematics and physics. By applying machine learning to complex theoretical data, such as knot invariants or integer sequences, we aim to uncover hidden patterns. A key emphasis of our work is explainability: when AI discovers or solves, we would like to know how.