Edward Frenkel is a renowned mathematician, professor of University of California, Berkeley, member of the American Academy of Arts and Sciences, and winner of the Herman Weyl Prize in Mathematical Physics. In this episode, Edward Frenkel discusses the recent monumental proof in the Langlands program, explaining its significance and how it advances understanding in modern mathematics.

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LINKS:•⁠ 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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TIMESTAMPS:00:00 - Edward’s Previous Appearance on TOE01:15 - Discoveries in Mathematics04:31 - Langland’s Program11:02 - Counting Problem14:58 - Symmetries of the Unit Disc26:55 - Part 1 of Edward’s Talk30:20 - Shimura-Taniyama-Weil Conjecture40:02 - Quick Recap42:38 - Langlands Dual Group51:50 - Rosetta Stone of Math01:00:10 - Riemann Surfaces01:10:20 - Proof of the Geometric Langlands Conjecture01:21:42 - Tribute to Legends01:26:02 - Langlands Correspondence for Riemann Surface01:43:30 - Galois Groups01:53:33 - Other Objects Involved02:10:40 - Outro / Support TOE

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