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Elementary Introduction to the Langlands Program, by Edward Frenkel

"Do we discover mathematics or do we invent it?"

One of the most fascinating and important developments in mathematics in the last 50 years is the Langlands Program, a collection of ideas that provides a grand unification of many areas of mathematics.

Edward Frenkel
is a professor of mathematics at the University of California, Berkeley, which he joined in 1997 after being on the faculty at Harvard University. He is a member of the American Academy of Arts and Sciences, a Fellow and a member of the Council of the American Mathematical Society, and the winner of the Hermann Weyl Prize in mathematical physics. Frenkel has authored three books and over eighty scholarly articles in academic journals, and he has lectured on his work around the world. His YouTube videos have garnered over 4 million views combined as of 2016. Frenkel’s book Love and Math was a New York Times bestseller, has been named one of the Best Books of the year by both Amazon and iBooks, and won the Euler Book Prize from the Mathematical Association of America. As of February 2016, it has been published in 16 languages.

In September 2015, Edward Frenkel gave a series of four lectures at MSRI, "Elementary Introduction to the Langlands Program". The videos of the lectures, linked below, give a wonderful opportunity to hear the story of these ideas from a great expositor, covering topics from the basic ideas of symmetries and Fermat's last theorem to the recent works connecting the Langlands Program to dualities in quantum physics. The lectures were recorded and broadcast on the Japanese TV channel NHK in November-December 2015 in the "Luminous Classroom" series. The unedited videos below are of the lectures as presented at MSRI.

The archived Japanese TV channel NHK webpage dedicated to the lectures is here.

The original page for the workshop series can be viewed here.

View the NHK Program

The original NHK broadcast 4-part series is now available via YouTube. (Note that while the introduction is in Japanese, the lecture is in English.)

View the Original Lectures

These lectures are filmed in MSRI's Simons Auditorium, without the additional editing of the television broadcast. To clearly view the slides referenced in each lecture, download the accompanying PDF slide decks.