Edward Frenkel: The Langlands Proof That Changed Mathematics Forever

Theories of Everything with Curt Jaimungal

Curt Jaimungal

Physics, Philosophy, Society & Culture, Science

4.6 • 606 Ratings

🗓️ 2 October 2024

⏱️ 134 minutes

🔗️ Recording | iTunes | RSS

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Summary

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 TOE1:15 Discoveries in Mathematics4:31 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 Math1:00:10 Riemann Surfaces1:10:20 Proof of the Geometric Langlands Conjecture1:21:42 Tribute to Legends1:26:02 Langlands Correspondence for Riemann Surface1:43:30 Galois Groups1:53:33 Other Objects Involved2:10:40 Outro / Support TOESPONSORS:- I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOERESOURCES:- 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- Support TOE on Patreon: https://patreon.com/curtjaimungal- 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- 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 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. FOLLOW: Substack | Spotify | YouTube | Twitter Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

Transcript

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0:00.0	Professor Edward Frankel, thank you for coming on the podcast again. Welcome. The previous
0:05.2	part one, did fantastic, and it's an exposition into the Geometric Langland's recent proof.
0:11.2	That's right. Well, good to be back with you and with you, Kurt, and your dedicated audience
0:18.3	of your podcast, Theories of Everything, I was very pleased by the response
0:24.2	to our first part on the Langlass program. There was a lot of interest, it seems, and so it
0:30.3	confirmed what I expected that you have some of the most sophisticated people watching this
0:35.7	podcast, people who do not shy away from
0:38.5	technicalities, from the details of some mathematical theories. So I'm kind of, I'm really excited
0:44.6	about continuing along these lines and revealing more secrets of the Langlands program.
0:50.5	Oh, wonderful. So one of the questions, and by the way, I was happily surprised about the reception.
0:56.2	I knew it would be successful, but I didn't think the previous episode would be that successful.
1:00.7	So that was a pleasant surprise.
1:03.1	Definitely for me too. It feels like people are digging this stuff, and there was a lot of comments and, you know, good response to our first part.
1:12.9	So let's continue.
1:15.4	Okay, so professor, many people are tuning in and they're hearing these terms like geometric langlins correspondence, many unfamiliar terms, analytic langlins, number fields, galwa groups.
1:29.8	Explain why this recent proof is monumental. The way mathematics develops is that, it's like you're searching for something
1:37.1	in the dark room or, you know, in the dark space. We may be searching for a key, you know.
1:43.9	And you, the way you would proceed usually is that we're trying to imagine how things could
1:50.2	work out.
1:51.6	And this way we come up with some analogies first, and then maybe with some more specific
1:55.8	conjectures.
1:57.1	In today's conversation, we'll have both.
	...

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