Category Archives: Mathematics

Scholze on Torsion, Part I

Posted on June 16, 2013 by Persiflage

This is a sequel to this post, although as it turns out we still won’t actually get to anything substantial — or indeed anything beyond an introduction — in this post. Let me begin with some overview. Suppose that \(X … Continue reading →

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

En Passant II

Posted on June 15, 2013 by Persiflage

Let’s party like it’s 1995! The Boston conference on Fermat produced a wonderful book, but now you can watch the original videos. Some first impressions: some of you used to have more hair (not naming names). Forum of Mathematics Pi … Continue reading →

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

Scholze on Torsion 0

Posted on June 13, 2013 by Persiflage

This will be the first zeroth of a series of posts talking about Scholze’s recent preprint, available here. This is mathematics which will, no question, have more impact in number theory than any recent paper I can think of. The … Continue reading →

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

Elsevier’s answer to public criticism:

Posted on May 28, 2013 by Persiflage

The following was sent to editors for an Elsevier journal; a copy of the email mysteriously fell into my hands, and I reproduce it here (in part): Following discussions with the board and at Elsevier this year, we feel that … Continue reading →

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

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

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

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