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. SPONSOR (THE ECONOMIST): As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe Check out Edward Frenkel's New York Times Bestselling book "Love and Math" at https://amzn.to/4gPAVn1. Also, please consider following Edward on Linkedin at https://www.linkedin.com/in/edfrenkel/ 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 TOE'S TOP LINKS: - Support TOE on Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Listen to TOE on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Join TOE's Newsletter 'TOEmail' at https://www.curtjaimungal.org TIMESTAMPS: 00:00 - Edward’s Previous Appearance on TOE 01:15 - Discoveries in Mathematics 04:31 - 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 01:00:10 - Riemann Surfaces 01:10:20 - Proof of the Geometric Langlands Conjecture 01:21:42 - Tribute to Legends 01:26:02 - Langlands Correspondence for Riemann Surface 01:43:30 - Galois Groups 01:53:33 - Other Objects Involved 02:10:40 - Outro / Support TOE SPONSORS (please check them out to support TOE): - THE ECONOMIST: As a listener of TOE, you can now enjoy full digital access to The Economist. Get a 20% off discount by visiting: https://www.economist.com/toe - INDEED: Get your jobs more visibility at https://indeed.com/theories ($75 credit to book your job visibility) - HELLOFRESH: For FREE breakfast for life go to https://www.HelloFresh.com/freetheoriesofeverything - PLANET WILD: Want to restore the planet's ecosystems and see your impact in monthly videos? The first 150 people to join Planet Wild will get the first month for free at https://planetwild.com/r/theoriesofeverything/join or use my code EVERYTHING9 later. Other Links: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything