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 - ConclusionSPONSORS:- The Economist: 20% off discount – https://www.economist.com/toeRESOURCES:- 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/- Join My New Substack (Personal Writings): https://curtjaimungal.substack.com- Listen on Spotify: https://tinyurl.com/SpotifyTOE- Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join- Support TOE on Patreon: https://patreon.com/curtjaimungal- Twitter: https://twitter.com/TOEwithCurt- Discord Invite: https://discord.com/invite/kBcnfNVwqs
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