Author Archives: Persiflage

Understatement

Posted on May 27, 2013 by Persiflage

This supposition, the so-called Twin Prime Conjecture, is not necessarily obvious . “He wasn’t a big name, and I get the impression that he wasn’t one of the leading analytical number theorists,” said Richard Taylor, a respected mathematician and a … Continue reading →

Posted in Mathematics | Leave a comment

Bush, the Messiah (and Emma Kirkby)

Posted on May 22, 2013 by Persiflage

The title of this post is, in part, a public service message to use the Oxford comma. However, there is a thread (in my mind) linking the three titular subjects. The connection between George Bush and the Messiah is not … Continue reading →

Posted in Music, Politics | Tagged , , , , , | Leave a comment

Finiteness of the global deformation ring over local deformation rings

Posted on May 18, 2013 by Persiflage

(This post is the result of a conversation I had with Matt). Suppose that \(\overline{\rho}: G_{F} \rightarrow \mathrm{GL}_n(\mathbf{F})\) is a continuous mod-\(p\) absolutely irreducible Galois representation. For now, let’s assume that \(F/F^{+}\) is a CM field, and \(\overline{\rho}\) is essentially … Continue reading →

Posted in Mathematics | Tagged , , , , , | 5 Comments

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 →

Posted in Food, Waffle | Tagged , , , | Leave a comment

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 →

Posted in Mathematics | Tagged , , , , , | Leave a comment

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 →

Posted in Mathematics | Tagged , , , , | Leave a comment

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 →

Posted in Mathematics | Tagged , , , , , , , | Leave a comment

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 →

Posted in Mathematics, Waffle | Tagged , , , | Leave a comment

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 →

Posted in Mathematics | Tagged | Leave a comment

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 →

Posted in Mathematics | Tagged , , , , | Leave a comment