Mathematical Physics

The subject of the proposed research lies at the frontier between Pure Mathematics and Theoretical Physics. A central theme of our study is the interplay between a set of recently discovered universal algebraic structures in Geometry and Physics, that have deep and immediate implications in Algebraic Geometry, Topology, and Mathematical Physics. On the physics side, these mathematical structures underpin several theoretical models in relativistic quantum physics, typically by encoding the underlying hidden symmetries of the model at hand. Mathematically, they make a ubiquitous appearance in many, often far-separated areas of pure mathematics, where they hold the key to codify and understand the answer to central questions in such diverse subjects as Algebraic and Symplectic Geometry, Non-Linear Dynamics, Gauge Theory, and Topology.