Author Archives: galoisrepresentations

Irregular Lifts, Part II

This is the global counterpart to the last post. I was going to write this post in a more general setting, but the annoyances of general reductive groups got the better of me. Suppose we fix the following: A number … Continue reading

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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

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More or less OPAQUE

I recently talked with Lynnelle Ye (a soon to be graduating student of Mark Kisin) for a few hours about her thesis and related mathematics. In her thesis, she generalizes (in part) the work Liu-Wan-Xiao on the boundary (halo) of … Continue reading

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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

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Bristol 2005

(This is really just a supplement to this post.) The AIM model of conferences encourages real time collaboration, which is unusual as far as mathematical conferences go. But the ne plus ultra of such a conference (among those I have … Continue reading

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The spoils of Rio

Congratulations to Akshay and Peter — don’t spend all those loonies at once! (Actually, I’m not sure that’s a grammatically correct usage of the word loonies unless they pay the winners in the form of 15000 coins; possibly the Hawk … Continue reading

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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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