Author Archives: Persiflage

The Decline of Western Civilization

Posted on April 11, 2014 by Persiflage

I am often inclined on Saturdays to spend a few hours at the Brothers K cafe. I bring my laptop and some scratch paper, sip away on a cortado, and listen to music on my headphones as I work; it … Continue reading →

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Are Galois deformation rings Cohen-Macaulay?

Posted on April 2, 2014 by Persiflage

Hyman Bass once wrote a paper on the ubiquity of Gorenstein rings. The first time they arose in the context of Hecke algebras, however, was Barry’s Eisenstein ideal paper, where he proves (at prime level) that the completions \(\mathbf{T}_{\mathfrak{m}}\) are … Continue reading →

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Robert Coleman

Posted on March 25, 2014 by Persiflage

I was very sad to learn that, after a long illness with multiple sclerosis, Robert Coleman has just died. Robert’s influence on mathematics is certainly obvious to all of us in the field. Most of my personal interaction with him … Continue reading →

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The Thick Diagonal

Posted on March 14, 2014 by Persiflage

Suppose that \(F\) is an imaginary quadratic field. Suppose that \(\pi\) is a cuspidal automorphic form for \(\mathrm{GL}(2)/F\) of cohomological type, and let us suppose that it contributes to the cohomology group \(H^1(\Gamma,\mathbf{C})\) for some congruence subgroup \(\Gamma\) of \(\mathrm{GL}_2(\mathcal{O}_F)\). … Continue reading →

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The congruence subgroup property for thin groups.

Posted on March 9, 2014 by Persiflage

I finally had a chance to visit Yale, which (by various orderings) is the fanciest US university at which I had never given a talk (nor even visited). The town itself struck me, at first, as a cross between Oxford … Continue reading →

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Short thoughts on my visit to Berkeley

Posted on February 25, 2014 by Persiflage

The marine biologists at Monterey Bay Aquarium give their octopuses hand massages. So do the fishmongers at Eataly. It’s quite an experience to come face to face with this antediluvian monster:  Are you allowed to turn right on red in … Continue reading →

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Local crystalline deformation rings

Posted on February 8, 2014 by Persiflage

I just returned from a very pleasant conference in Puerto Rico courtesy of the Simons Foundation (general advice: if you live in Chicago, always accept invitations to conferences in January). One thing I learnt from Toby Gee was the following … Continue reading →

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Gross Fugue

Posted on January 11, 2014 by Persiflage

Here are some variations on the theme of the last post, which is also related to a problem of Dick Gross. In this post, I want to discuss weight one modular forms where the level varies in the “vertical” aspect … Continue reading →

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The mystery of the primes

Posted on January 4, 2014 by Persiflage

No, this is not the sequel to Marcus du Sautoy’s book, but rather a curious observation regarding George Schaeffer’s tables of “ethereal” weight one Katz modular eigenforms (which you can find starting on p.64 here). Let \(N\) be a positive … Continue reading →

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Daleks

Posted on December 5, 2013 by Persiflage

I’ve wanted to write a post about the new Doctor Who series for a while, but this is not that post. Instead, this post is about a Macintosh game called Daleks, which I first played on a Mac 512 (running … Continue reading →

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