Monthly Archives: September 2014

Applying for an NSF grant

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

Posted in Mathematics, Politics | Tagged , | 10 Comments

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

Let be an arbitrary number field. Let be a prime which splits completely in , and consider an absolutely irreducible representation: which is unramified outside finitely many primes. If one assumes that is geometric, then the Fontaine–Mazur conjecture predicts that … Continue reading

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Tricky Fingers

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

Posted in Music | Tagged , , | 3 Comments

The Artin conjecture is rubbish

Let be a continuous irreducible representation. Artin conjectured that the L-function is analytically continues to an entire function on (except for the trivial representation where the is a simple pole at one) and satisfies a functional equation of a precise … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , | 9 Comments

K_2(O_F) for number fields F

Belabas and Gangl have a nice paper ( Generators and relations for , which can be found here) where they compute for a large number of quadratic fields . There main result is a method for proving upper bounds for … Continue reading

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Intermezzo

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

Posted in Waffle | Tagged , , , , , , , | 5 Comments