Eva Miranda: The Mathematical Bridge Between Classical and Quantum

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:- I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://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- Crypto: https://nowpayments.io/donation/TOE- Twitter: https://twitter.com/TOEwithCurt- Discord Invite: https://discord.com/invite/kBcnfNVwqs Theories of Everything with Curt Jaimungal features long-form, technically detailed interviews with leading researchers in physics, mathematics, consciousness, and philosophy, exploring topics at the level of active research. For academics, graduate students, and anyone seeking depth beyond popular science. Learn more about your ad choices. Visit megaphone.fm/adchoices