Tag Archives: RLT

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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MSRI Now

Continuing on the theme of the last post (Buzzard related viral videos), you can now view Buzzard’s MSRI course (in progress at the time of this post) online here. Having previously excoriated MSRI for restricting how many people can attend … 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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A non-liftable weight one form modulo p^2

I once idly asked RLT (around 2004ish) whether one could use Buzzard-Taylor arguments to prove that any representation: which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). Galois representations of this flavour … Continue reading

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Serre 1: Calegari 0

I just spent a week or so trying to determine whether Serre’s conjecture about the congruence subgroup property was false for a very specific class of S-arithmetic groups. The punch line, perhaps not surprisingly, was that I had made an … Continue reading

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Random Photos

Lunt Hall, the Northwestern mathematics building, ¬†recently underwent an upgrade of the fire alarm system. This includes introducing informative new signage, such as the following: Another change is that the “internal” window to my office was boarded up. The window … Continue reading

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