The classical and quantum worlds are not as apart as we thought.

Eva Miranda, a renowned researcher in symplectic and Poisson geometry, explains how “hidden” geometric structures can unite classical and quantum frameworks. Eva dives into integrable systems, Bohr–Sommerfeld leaves, and the art of geometric quantization, revealing a promising path to bridging longstanding gaps in theoretical physics.

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Links Mentioned:

•⁠ ⁠Eva Miranda’s website: https://web.mat.upc.edu/eva.miranda/nova/

•⁠ ⁠Roger Penrose on TOE: https://www.youtube.com/watch?v=sGm505TFMbU

•⁠ ⁠Curt’s post on LinkedIn: https://www.linkedin.com/feed/update/urn:li:activity:7284265597671034880/

Timestamps:

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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