Author Archives: Persiflage

I don’t know how to prove Serre’s conjecture.

Posted on May 30, 2014 by Persiflage

I find it slightly annoying that I don’t know how to prove Serre’s conjecture for imaginary quadratic fields. In particular, I don’t even see any particularly good strategy for showing that a surjective Galois representation — say finite flat with … Continue reading →

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Thurston, Selberg, and Random Polynomials, Part II.

Posted on May 24, 2014 by Persiflage

What is the probability that the largest root of a polynomial is real? Naturally enough, this depends on how one models a random polynomial. If we take polynomials of degree N which are constrained to have all of their roots … Continue reading →

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Thurston, Selberg, and Random Polynomials, Part I.

Posted on May 21, 2014 by Persiflage

Apart from everything else, you could always count on Bill Thurston to ask interesting questions. This is the first of a small number of posts which were motivated in part by figure two from this paper, and this accompanying MO … Continue reading →

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A postview of Bellairs/Barbados

Posted on May 14, 2014 by Persiflage

I am just recovering from my trip to Barbados for the McGill sponsored conference at the Bellairs institute (which I previously discussed here). I thought it was a wonderfully enjoyable conference, for many reasons. The first is that I got … Continue reading →

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Are business schools intellectually bankrupt?

Posted on May 11, 2014 by Persiflage

From the New York Times today, a report from business school professors concerning a study which claims to show that professors are prejudiced, too. I remember reading the original paper on this study, which made it painfully clear that the … Continue reading →

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A Preview of Barbados/Bellairs

Posted on April 21, 2014 by Persiflage

This post is probably not so interesting unless you plan to travel to the Caribbean in a few weeks. The website for the conference is offline, so I thought I might update attendees on what might be happening, at least … Continue reading →

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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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