Author Archives: Persiflage

Michael Pollan is not a scientist

Posted on May 16, 2013 by Persiflage

Michael Pollan is popular because he is an engaging speaker who spins a narrative about food that dovetails with the political inclinations of his audience. He has a degree in English, and, as far as I know, no scientific training … Continue reading →

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Equidistribution of Heegner Points

Posted on May 15, 2013 by Persiflage

I saw a nice talk by Matt Young recently (joint work with Sheng-Chi Liu and Riad Masri) on the following problem. For a fundamental discriminant \(|D|\) of an imaginary quadratic field \(F\), one has \(h_D\) points in \(X_0(1)(\mathbf{C})\) with complex … Continue reading →

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Exercise concerning quaternion algebras

Posted on May 11, 2013 by Persiflage

Here’s a fun problem that came up in a talk by Jacob Tsimerman on Monday concerning some joint work with Andrew Snowden: Problem: Let \(D/\mathbf{Q}(t)\) be a quaternion algebra such that the specialization \(D_t\) splits for almost all \(t\). Then … Continue reading →

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Catalan’s Constant and periods

Posted on May 4, 2013 by Persiflage

There is a 60th birthday conference in honour of Frits Beukers in Utrech in July; I’m hoping to swing by there on the way to Oberwolfach. Thinking about matters Beukers made me reconsider an question that I’ve had for while. … Continue reading →

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Exposition is not underrated

Posted on April 28, 2013 by Persiflage

It seems to be the conventional wisdom (for example, some of the comments here) that exposition is undervalued in our profession. I disagree. To cast things in economic terms, let’s take “valued” to mean one of two things: increased salary … Continue reading →

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Galois Representations for non-self dual forms, Part III

Posted on April 27, 2013 by Persiflage

Here are some complements to the previous remarks, considered in Part I and Part II. First, in order to deal with non-zero weights, one has to replace the Shimura varieties \(Y\), \(X\), \(W\) by Kuga-Satake varieties over these spaces. This … Continue reading →

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Inverse Galois Problem

Posted on April 24, 2013 by Persiflage

My favourite group as far as the inverse Galois problem goes is \(G = \mathrm{SL}_2(\mathbf{F}_p)\). This is not known to be a Galois group over \(\mathbf{Q}\) for any \(p > 13\), the difficulty of course being that is must correspond … Continue reading →

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Galois Representations for non self-dual forms, Part II

Posted on April 21, 2013 by Persiflage

(Now with updates!) Let’s recap from part I. We have a Shimura variety \(Y\), a minimal projective compactification \(X\), and a (family of) smooth toroidal compactifications \(W\). We also have Galois representations of the correct shape associated to eigenclasses in … Continue reading →

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Cambridge Days

Posted on April 10, 2013 by Persiflage

Dinner at the Helmand: Zagat rating 27 (Food) and 20 (Service). After I was seated, it was fifteen minutes until I was brought a menu. Sixty seconds later, the waitress asked what I wanted to order, and then pouted when … Continue reading →

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Galois Representations for non self-dual forms, Part I

Posted on March 26, 2013 by Persiflage

This is the first of a series of posts discussing the recent work of Harris, Lan, Taylor, and Thorne on constructing Galois representations associated to regular algebraic automorphic forms for \(\mathrm{GL}(n)\) over a CM field \(F/F^{+}\). I will dispense with … Continue reading →

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