Tag Archives: Toby Gee

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

Posted in Mathematics | Tagged , , , , , , , , | 6 Comments

Mazur’s Program B on Abelian Surfaces

In the book “More mathematical people,” there is an interview with Robin Wilson with the following quote: At the meal I found myself sitting next to Alistair Cooke who was very charming, and absolutely fascinating to listen to. The very … Continue reading

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

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

Mazur 80

Last week I was in Cambridge for Barry’s 80th birthday conference. If you are wondering why it took so long for Barry to get a birthday conference, that’s probably because you didn’t know that there was *also* a 60th birthday … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 16 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 over … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , | 6 Comments

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

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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments