Monthly Archives: October 2012

How I deal with technical support

Posted on October 31, 2012 by Persiflage

I usually manage to avoid having to make any of those annoying calls to banks, credit card companies, utility companies, etc. because DW does it all for me. However, there are times (for example, when things are in my name) … Continue reading →

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Schoenberg

Posted on October 28, 2012 by Persiflage

The best show on television…is surely classic arts showcase. It’s RAGE for classical music, by which I mean something like an eclectic classical music version of MTV (during the 80’s). Given the limited range of classical music that makes it … Continue reading →

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Jacobi by pure thought

Posted on October 26, 2012 by Persiflage

JB asks whether there is a conceptual proof of Jacobi’s formula: \(\Delta = q \prod_{n=1}^{\infty}(1 – q^n)^{24}\) Here (to me) the best proof is one that requires the least calculation, not necessarily the “easiest.” Here is my attempt. We use … Continue reading →

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En Passant

Posted on October 24, 2012 by Persiflage

Several times in NYC, I’ve had the chance to visit Eataly, an italian food court/upscale delicatessen run by Mario Batali. You can either sit down at one of the various restaurants for an antipasto plate with a glass of wine, … Continue reading →

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Prokofiev

Posted on October 21, 2012 by Persiflage

Glenn Gould is best known (deservedly) for his Bach, but there are other treasures in his discography, including Schoenberg and (perhaps surprisingly) Brahms. Here’s Gould playing some mean Prokofiev:

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Remarks on Buzzard-Taylor

Posted on October 18, 2012 by Persiflage

Let \(\rho: G_{\mathbf{Q},S} \rightarrow \mathrm{GL}_2(\overline{\mathbf{Q}}_p)\) be continuous and unramified at \(p\). The Fontaine-Mazur conjecture predicts that \(\rho\) has finite image and is automorphic. Buzzard and Taylor proved this result under the assumption the natural assumption that \(\rho\) is odd, that … Continue reading →

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Winning the Chocolate

Posted on October 18, 2012 by Persiflage

Once a month, there is an (unrated) round robin blitz tournament at the Evanston chess club. The time controls are set on five minutes (a little slow for me, I usually play one minute games online), but it’s nice to … Continue reading →

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Why it is good to be Pure

Posted on October 15, 2012 by Persiflage

There do not exist any regular pure motives \(M\) over \(\mathbf{Q}\) which are not essentially self dual. Here is why. \(M\) gives rise to a compatible family of Galois representations for each rational prime \(v\) such that the characteristic polynomial … Continue reading →

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Hilbert Modular Forms of Partial Weight One, Part I

Posted on October 13, 2012 by Persiflage

Let \(\pi\) be an algebraic Hilbert modular cuspform for some totally real field \(F^{+}\). Then, associated to \(\pi\), one has a compatible family of Galois representations: \(r_{\lambda}(\pi): G_{F^{+}} \rightarrow \mathrm{GL}_2(\mathcal{O}_{\lambda})\) which are unramified outside finitely many primes (this is the … Continue reading →

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Even Galois Representations mod p

Posted on October 7, 2012 by Persiflage

Suppose that \(\overline{\rho}: G_{\mathbf{Q}}: \rightarrow \mathrm{GL}_2(\overline{\mathbf{F}}_p)\) is a continuous  irreducible Galois representation. What does the Langlands program say about such \(\overline{\rho}\)? When \(\overline{\rho}\) is odd, the situation is quite satisfactory, the answer being given by Serre’s conjecture. For example, having fixed a … Continue reading →

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