Eva Miranda explains how hidden geometric structures can unite classical and quantum physics, exploring integrable systems, Bohr‑Sommerfeld leaves, and geometric quantization. The conversation reveals a promising path toward bridging long‑standing gaps in theoretical physics.
- 00:00 - Introduction
- 06:12 - Classical vs. Quantum Mechanics
- 15:32 - Poisson Brackets & Symplectic Forms
- 24:14 - Integrable Systems
- 32:01 - Dirac’s Dream & No‑Go Results
- 39:04 - Action‑Angle Coordinates
- 47:05 - Toric Manifolds & Polytopes
- 54:55 - Geometric Quantization Basics
- 1:03:46 - Bohr‑Sommerfeld Leaves
- 1:12:03 - Handling Singularities
- 1:20:23 - Poisson Manifolds Beyond Symplectic
- 1:28:50 - Turing Completeness & Fluid Mechanics Tie‑In
- 1:35:06 - Topological QFT Overview
- 1:45:53 - Open Questions in Quantization
- 1:53:20 - Conclusion
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