Ph.D. Public Lecture (Math) - Manimugdha Saikia

Title: Complex Hyperbolic Geometry and Geometric Quantization

Abstract: In geometric quantization, a commonly studied topic is exploring the correspondence between various submanifolds of classical phase space (modeled as a symplectic manifold) and the corresponding (quantum) states. In this talk, we shall discuss very briefly about geometric quantization and see one such correspondence. But first we shall discuss one of the most famous models of complex hyperbolic geometry, namely the unit ball model. Then we introduce relevant definitions and examples related to Kahler manifolds; and two of the widely used measures of Information Theory, namely the entropy of entanglement and the entanglement of formation. Finally, we shall see a result (by Barron, Wheatley) that gives us a relationship between the geometry of certain submanifolds and the corresponding states.