Tag Archives: Toby Gee

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

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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

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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

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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

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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. Recal that, for a smooth projective variety X over a number field F unramified outside … Continue reading

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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

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New Results In Modularity, Part I

I usually refrain from talking directly about my papers, and this reticence stems from wishing to avoid any appearance of tooting my own horn. On the other hand, nobody else seems to be talking about them either. Moreover, I have … Continue reading

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