Tag Archives: Patrick Allen

Counting solutions to a_p = λ, Part II

Posted on March 3, 2020 by Persiflage

This is a sequel to this post where the problem of counting eigenforms with \(a_p = \lambda\) and \(\lambda \ne 0\) was considered. Here we report on recent progress in the case \(\lambda = 0\). It is a somewhat notorious … Continue reading →

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New Results in modularity, Christmas Update II

Posted on December 30, 2019 by Persiflage

Just like last year, once again saint Nick has brought us a bounty of treasures related to Galois representations and automorphic forms in the final week of the year. First there was this paper by Newton and Thorne, proving, among … Continue reading →

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Hausdorff Trimester Summer School, May 11-15, 2020

Posted on September 26, 2019 by Persiflage

This post is to encourage both PhD students and any junior researchers who are interested to consider applying to a summer school on the arithmetic of the Langlands Program. (Some financial support will be available.) This is the first event … Continue reading →

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Local-global compatibility for imaginary quadratic fields

Posted on January 16, 2019 by Persiflage

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 →

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New Results In Modularity, Christmas Update

Posted on December 25, 2018 by Persiflage

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 →

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Update on Sato-Tate for abelian surfaces

Posted on July 19, 2018 by Persiflage

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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Graduation Day

Posted on November 26, 2017 by Persiflage

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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New Results in Modularity, Part II

Posted on June 23, 2017 by Persiflage

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

Posted on June 23, 2017 by Persiflage

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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