Author Archives: Persiflage

Derived Langlands

Posted on December 22, 2014 by Persiflage

Although it has been in the air for some time, it seems as though ideas from derived algebraic geometry have begun to inform developments in the Langlands program. (A necessary qualifier: I am talking about reciprocity in the classical arithmetic … Continue reading →

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Harris 60

Posted on December 15, 2014 by Persiflage

I’ve just returned from the excellent MSRI workshop which honored Michael Harris’ 60th birthday, and here is a brief summary of some of the gossip and mathematics I picked up when I was there. First, let me take note of … Continue reading →

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The Modular Forms Database is Annoying

Posted on November 23, 2014 by Persiflage

It used to be the case, 10 or so years ago, that William Stein maintained a website with extensive tables of \(q\)-expansions of modular forms, computed using magma. However, as the edifice of civilization begins to crumble, this website no … Continue reading →

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Mysterious Formulae

Posted on November 15, 2014 by Persiflage

I’m not one of those mathematicians who is in love with abstraction for its own sake (not that there’s anything wrong with that). I can still be seduced by an explicit example, or even — quell horreur — a definite … Continue reading →

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In Brief

Posted on October 21, 2014 by Persiflage

The start of the academic year has a habit of bringing forth distractions, not least of all to someone as disorganized as me. So here are a few remarks in brief. The class number of \(\mathbf{Q}(\zeta_{151})^{+}\) is one. John Miller, … Continue reading →

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iTunes top Ten

Posted on October 6, 2014 by Persiflage

tl;dr: lots of Bach, if you’re not into that sort of thing, at least check out Mel Brooks. And if you’re not into that *either*, well then I don’t know what’s wrong with you. Following Jordan, here is a list … Continue reading →

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Applying for an NSF grant

Posted on September 26, 2014 by Persiflage

It’s not easy to write a good grant proposal. But it can be even harder to write one for the first time, especially if you’re not quite sure who will be reading your proposal. So today, I want to say … Continue reading →

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The nearly ordinary deformation ring is (usually) torsion over weight space

Posted on September 19, 2014 by Persiflage

Let \(F/{\mathbf{Q}}\) be an arbitrary number field. Let \(p\) be a prime which splits completely in \(F\), and consider an absolutely irreducible representation: \(\rho: G_{F} \rightarrow {\mathrm{GL}}_2({\overline{\mathbf{Q}}}_p)\) which is unramified outside finitely many primes. If one assumes that \(\rho\) is … Continue reading →

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Tricky Fingers

Posted on September 18, 2014 by Persiflage

How is one supposed to play this exactly? One can neither can play a 14th in the right hand (my hands are not that big) nor play legato parallel 10ths in the left; hence some sort of arpeggiation is required. … Continue reading →

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The Artin conjecture is rubbish

Posted on September 10, 2014 by Persiflage

Let \(\rho: G_{\mathbf{Q}} \rightarrow \mathrm{GL}_N(\mathbf{C})\) be a continuous irreducible representation. Artin conjectured that the L-function \(L(\rho,s)\) is analytically continues to an entire function on \(\mathbf{C}\) (except for the trivial representation where the is a simple pole at one) and satisfies … Continue reading →

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