Author Archives: Persiflage

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 →

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Thoughts on Paris

Posted on May 25, 2017 by Persiflage

Nothing is more pretentious or annoying than when an American offers, uninvited, their opinions of Paris. Here, then, are some of mine. Starting the day with a two hour lecture on elliptic integals:OUI: Who does not get a slight frisson … Continue reading →

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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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Return to Northwestern

Posted on April 21, 2017 by Persiflage

Today I returned to Northwestern, taking part in both the communal faculty lunch and the post prandial espresso. Jared Wunsch worked his magic on the Silvia (Rancilio) to pour one of the best espressos I have had in a very … Continue reading →

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Me versus Magnus

Posted on April 2, 2017 by Persiflage

I’ve recently been distracting myself with the new Magnus Carlsen “app,” a free chess app for the iPhone whose distinguishing feature is that it tries to play “like” Magnus did at various ages. It does seem like a very tricky … 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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Erdős Number 3!

Posted on March 26, 2017 by Persiflage

My chances at this point of writing a paper with Erdős are probably very small. My chances of writing a paper with one of Erdős’ collaborators is also quite small. I had assumed that I had not even met — … Continue reading →

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Film Criticism

Posted on March 22, 2017 by Persiflage

You know that feeling you get when you want to understand the precise conjectural relationship between the cohomology of arithmetic varieties and Galois representations? I finally get it. Du musst Caligari werden! Oh, and if you think I’m crazy, it’s … 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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Report from MSRI and Berkeley

Posted on March 7, 2017 by Persiflage

Having attended last Friday’s academic sponsors’ day at MSRI, I can provide a little more context concerning the issues expressed last time. But first, it’s time for the current edition of NAME AND SHAME: There are currently 105 universities which … Continue reading →

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