Edward Frenkel: The Langlands Proof That Changed Mathematics Forever

Edward Frenkel, a leading mathematician, explains the recent monumental proof in the Langlands program and its impact on modern mathematics. He also revisits earlier work and connects the breakthrough to broader themes in geometry and physics.

0:00 Edward's Previous Appearance on TOE
1:15 Discoveries in Mathematics
4:31 Langland's Program
11:02 Counting Problem
14:58 Symmetries of the Unit Disc
26:55 Part 1 of Edward's Talk
30:20 Shimura-Taniyama-Weil Conjecture
40:02 Quick Recap
42:38 Langlands Dual Group
51:50 Rosetta Stone of Math
1:00:10 Riemann Surfaces
1:10:20 Proof of the Geometric Langlands Conjecture
1:21:42 Tribute to Legends
1:26:02 Langlands Correspondence for Riemann Surface
1:43:30 Galois Groups
1:53:33 Other Objects Involved
2:10:40 Outro / Support TOE

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RESOURCES:

- Edward Frenkel's New York Times Bestselling book "Love and Math": https://amzn.to/4gPAVn1
- Edward on Linkedin: https://www.linkedin.com/in/edfrenkel/
- Edward Frenkel's Twitter: https://x.com/edfrenkel
- Edward Frenkel's Official Website: https://edwardfrenkel.com
- Edward Frenkel's YouTube: https://youtube.com/@edfrenkel
- Edward Frenkel's Instagram: https://www.instagram.com/edfrenkel
- Edward Frenkel’s SoundCloud (DJ Moonstein): https://soundcloud.com/moonstein
- Edward Frenkel's 1st TOE Episode: https://www.youtube.com/watch?v=n_oPMcvHbAc
- Andre Weil’s letter on “Rosetta Stone” of Math: https://www.ams.org/notices/200503/fea-weil.pdf
- "Proof of the Geometric Langlands Conjecture" (Papers): https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
- Etingof-Frenkel-Kazhdan, “A general framework for the Analytic Langlands Correspondence”: https://arxiv.org/abs/2311.03743
- Yuri Manin’s book “Mathematics and Physics”: https://www.amazon.com/Mathematics-Physics-Progress-Mathematical/dp/1489967842
- Edward Frenkel’s papers: https://edwardfrenkel.com/frenkel-biblio.pdf
- Edward Frenkel’s previous lecture on TOE (Part 1): https://www.youtube.com/watch?v=RX1tZv_Nv4Y
- Mathematics and Physics (book): https://www.amazon.com/Mathematics-Physics-Progress-English-Russian/dp/3764330279
- Richard Borcherds on TOE: https://www.youtube.com/watch?v=U3pQWkE2KqM
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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.

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