Category Archives: Mathematics

Mathieu Magic

Posted on October 16, 2017 by Persiflage

I previously mentioned that I once made (in a footnote) the false claim that for a 11-dimensional representation V of the Mathieu group M_12, the 120 dimensional representation Ad^0(V) was irreducible. I had wanted to write down representations W of … Continue reading →

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The True Heirs To Ramanujan

Posted on September 19, 2017 by Persiflage

If you are in need of some light relief, you could do worse than peruse the opinions of Doron Zeilberger, who, if viewed strictly through the lens of these ramblings, appears to have a relationship with theoretical mathematics something along … Continue reading →

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Public Displays of Mathematics

Posted on August 25, 2017 by Persiflage

Let me start by saying that I’m in favor of making the effort to both educate the public about mathematics (as well as science more generally) and to convey to them a sense of the excitement of our discipline. But … Continue reading →

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MSRI Now

Posted on July 29, 2017 by Persiflage

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

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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Elementary Class Groups Updated

Posted on June 10, 2017 by Persiflage

In a previous post, I gave a short argument showing that, for odd primes p and N such that \(N \equiv -1 \mod p,\) the p-class group of \(\mathbf{Q}(N^{1/p})\) is non-trivial. This post is just to remark that the same … Continue reading →

Posted in Mathematics | 4 Comments

Who proved it first?

Posted on April 25, 2017 by Persiflage

During Joel Specter’s thesis defense, he started out by remarking that the \(q\)-expansion: \(\displaystyle{f = q \prod_{n=1}^{\infty} (1 – q^n)(1 – q^{23 n}) = \sum a_n q^n}\) is a weight one modular forms of level \(\Gamma_1(23),\) and moreover, for \(p\) … Continue reading →

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Pseudo-representations and the Eisenstein Ideal

Posted on March 29, 2017 by Persiflage

Preston Wake is in town, and on Tuesday he gave a talk on his recent joint work with Carl Wang Erickson. Many years ago, Matt and I studied Mazur’s Eisenstein Ideal paper from the perspective of Galois deformation rings. Using … Continue reading →

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A non-liftable weight one form modulo p^2

Posted on March 10, 2017 by Persiflage

I once idly asked RLT (around 2004ish) whether one could use Buzzard-Taylor arguments to prove that any representation: \(\rho: \mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q}) \rightarrow \mathrm{GL}_2(\mathbf{Z}/p^2 \mathbf{Z})\) which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). … Continue reading →

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