Monthly Archives: September 2014

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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K_2(O_F) for number fields F

Posted on September 4, 2014 by Persiflage

Belabas and Gangl have a nice paper ( Generators and relations for \(K_2({\mathcal{O}}_F)\), which can be found here) where they compute \(K_2({\mathcal{O}}_E)\) for a large number of quadratic fields \(E\). There main result is a method for proving upper bounds … Continue reading →

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Intermezzo

Posted on September 3, 2014 by Persiflage

Scholze is giving a course at Berkeley! Follow Jared Weinstein’s lecture notes from the course here. I believe that the lectures are also being recorded and will be available approximately one week after each lecture; I will add a link … Continue reading →

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