Tag Archives: Ana Caraiani

Local-global compatibility for imaginary quadratic fields

One of the key steps in the 10-author paper is to prove results on local-global compatibility for Galois representations associated to torsion classes. The results proved in that paper, unfortunately, fall well-short of the optimal desired local-global compatibility statement, because … Continue reading

Posted in Uncategorized | Tagged , , , , , , , , , , , , | 5 Comments

New Results In Modularity, Christmas Update

It’s a Christmas miracle! Keen watchers of this blog will be happy to learn that the 10 author paper discussed here and here is now available. (And just in case you also missed it, you can also find the other … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , | 7 Comments

Hausdorff Trimester: May 4-August 21, 2020

This post is to let everyone know that there will be a trimester at the Hausdorff institute in 2020 organized by Ana Caraiani, Laurent Fargues, Peter Scholze, and myself on “The Arithmetic of the Langlands Program“. The dates for both … Continue reading

Posted in Mathematics | Tagged , , , , , , | Leave a comment

Update on Sato-Tate for abelian surfaces

Various people have asked me for an update on the status of the Sato-Tate conjecture for abelian surfaces in light of recent advances in modularity lifting theorems. My student Noah Taylor has exactly been undertaking this task, and this post … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Upcoming Attractions

There’s a packed schedule for graduate classes at Chicago next Fall: Ngô Bảo Châu on automorphic forms (TueTh 11:00-12:30), Akhil Mathew on perfectoid spaces (MWF 12:30-1:30), and George Boxer and me on (higher) Hida theory (MW 1:30-3:00). Strap yourself in! … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , | 1 Comment

Abelian Surfaces are Potentially Modular

Today I wanted (in the spirit of this post) to report on some new work in progress with George Boxer, Toby Gee, and Vincent Pilloni. Edit: The paper is now available here. Recal that, for a smooth projective variety X … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

New Results in Modularity, Part II

This is part two of series on work in progress with Patrick Allen, Ana Caraiani, Toby Gee, David Helm, Bao Le Hung, James Newton, Peter Scholze, Richard Taylor, and Jack Thorne. Click here for Part I It has been almost … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 7 Comments