Category Archives: Langlands

All Langlands, all the time

Posted on October 3, 2024 by woit

Trying to keep track of everything happening in the Langlands program area of mathematics is somewhat of a losing battle, as new ideas and results keep appearing faster than anyone could be expected to follow. Here are various items: Dennis … Continue reading →

Posted in Langlands | 6 Comments

Two More

Posted on August 13, 2024 by woit

Two more items: I can’t recommend strongly enough that you watch the new Curt Jaimungal podcast with Edward Frenkel. The nominal topic is the recent proof of the geometric Langlands conjecture, but this is introductory material, with geometric Langlands and … Continue reading →

Posted in Langlands, Uncategorized | 13 Comments

A Few Items

Posted on July 2, 2024 by woit

A few items, all involving Peter Scholze in one way or another: A seminar in Bonn on Scholze’s geometrization of real local Langlands is finishing up next week. This is working out details of ideas that Scholze presented at the … Continue reading →

Posted in abc Conjecture, Langlands | 14 Comments

Various and Sundry

Posted on April 28, 2024 by woit

The semester here is coming to a close. I’m way behind writing up notes for the lectures I’ve been giving, which are ending with covering the details of the Standard Model. This summer I’ll try to finish the notes and … Continue reading →

Posted in Euclidean Twistor Unification, Langlands | 14 Comments

A New Approach to Modularity

Posted on February 28, 2024 by woit

I was assuming that Peter Scholze’s Emmy Noether lectures at the IAS would be the big news about advances in the Langlands program this coming week, but an anonymous correspondent just sent me this link. Tomorrow Andrew Wiles will be … Continue reading →

Posted in Langlands | 4 Comments

Arithmetic, Geometry and QFT news

Posted on February 5, 2024 by woit

This week at Harvard’s CMSA there’s a program on Arithmetic Quantum Field Theory that is starting up and will continue through March. There’s a series of introductory talks going on this week, by Minhyong Kim, Brian Williams, and David Ben-Zvi. … Continue reading →

Posted in Langlands | 10 Comments

Analytic Stacks

Posted on October 19, 2023 by woit

Dustin Clausen and Peter Scholze are giving a course together this fall on Analytic Stacks, with Clausen lecturing at the IHES, Scholze from Bonn. Here’s the syllabus: The purpose of this course is to propose new foundations for analytic geometry. … Continue reading →

Posted in Langlands | 13 Comments

What Does Spec Z Look Like?

Posted on September 14, 2023 by woit

This week Laurent Fargues has started a series of lectures here at Columbia on Some new geometric structures in the Langlands program. Videos are available here, but unfortunately there is a problem with the camera in that room, making the … Continue reading →

Posted in Langlands | 24 Comments

Relative Langlands Duality

Posted on July 10, 2023 by woit

For several years now, David Ben-Zvi, Yiannis Sakellaridis and Akshay Venkatesh have been working on a project involving a relative version of Langlands duality, which among many other things provides a perspective on L-functions and periods of automorphic forms inspired … Continue reading →

Posted in Langlands | 4 Comments

The Work of Robert Langlands

Posted on July 6, 2023 by woit

This is more of an advertisement than a blog post. This evening on the arXiv James Arthur has posted a wonderful 204 page document explaining the work of Robert Langlands, written in conjunction with the award of the Abel Prize … Continue reading →

Posted in Langlands | 1 Comment