Exploring Langlands Duality

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 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

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#science #physics #math #podcast #sciencepodcast #maths

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