Tag Archives: Ana Caraiani

The future is now; recap from Cetraro

Posted on July 31, 2022 by Persiflage

I’ve just returned from the second Journal of Number Theory biennial conference in Italy. It’s always nice to get a chance to see slices of number theory one wouldn’t otherwise see at the conferences I usually go to (although this … Continue reading →

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30 years of modularity: number theory since the proof of Fermat

Posted on July 8, 2022 by Persiflage

It’s probably fair to say that the target audience for this blog is close to orthogonal to the target audience for my talk, but just in case anyone wants to watch it in HD (and with the audio synced to … 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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Dembélé on Abelian Surfaces with good reduction everywhere

Posted on March 27, 2019 by Persiflage

New paper by Dembélé (friend of the blog) on abelian surfaces with good reduction everywhere (or rather, the lack of them for many real quadratic fields of small discriminant). I have nothing profound to say about the question of which … 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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Hausdorff Trimester: May 4-August 21, 2020

Posted on November 18, 2018 by Persiflage

This post is to let everyone know that there will be a trimester at the Hausdorff institute in 2020 organized by Ana Caraiani, Laurent Fargues, Peter Scholze, and myself on “The Arithmetic of the Langlands Program“. The dates for both … 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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Upcoming Attractions

Posted on May 11, 2018 by Persiflage

There’s a packed schedule for graduate classes at Chicago next Fall: Ngô Bảo Châu on automorphic forms (TueTh 11:00-12:30), Akhil Mathew on perfectoid spaces (MWF 12:30-1:30), and George Boxer and me on (higher) Hida theory (MW 1:30-3:00). Strap yourself in! … Continue reading →

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Abelian Surfaces are Potentially Modular

Posted on November 11, 2017 by Persiflage

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 →

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