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Meta
Tag Archives: Toby Gee
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
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
Irregular Lifts, Part I
This post motivated in part by the recent preprint of Fakhruddin, Khare, and Patrikis, and also by Matt’s number theory seminar at Chicago this week. (If you are interested in knowing what the calendar is for the Chicago number theory … Continue reading
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, Students
Tagged Ana Caraiani, Andrew Sutherland, Andrew Wiles, Bao Le Hung, Christian Johansson, David Helm, Francesc Fité, Freydoon Shahidi, George Boxer, Henry Kim, Jack Thorne, James Newton, Kiran Kedlaya, Laurent Clozel, Michael Harris, Nick Katz, Noah Taylor, Patrick Allen, Peter Scholze, Potential Modularity, Richard Taylor, Sato-Tate, Serre, Toby Gee, Victor Rotger, Vincent Pilloni
3 Comments
The paramodular conjecture is false for trivial reasons
(This is part of a series of occasional posts discussing results and observations in my joint paper with Boxer, Gee, and Pilloni mentioned here.) Brumer and Kramer made a conjecture positing a bijection between isogeny classes of abelian surfaces \(A/\mathbf{Q}\) … Continue reading
Graduation Day
This last summer, I undertook my last official activity as a faculty member at Northwestern University, namely, graduation day! (I had a 0% courtesy appointment for two years until my last Northwestern students graduated.) Here I am with four of … Continue reading