Author Archives: galoisrepresentations

New Results in Modularity, Part II

This is part two of series on work in progress with Patrick Allen, Ana Caraiani, Toby Gee, David Helm, Bao Le Hung, James Newton, Peter Scholze, Richard Taylor, and Jack Thorne. Click here for Part I It has been almost … Continue reading

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New Results In Modularity, Part I

I usually refrain from talking directly about my papers, and this reticence stems from wishing to avoid any appearance of tooting my own horn. On the other hand, nobody else seems to be talking about them either. Moreover, I have … Continue reading

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In defense of Theresa May

Nothing gives me more sympathy for Theresa May^* (or less respect for the Economist) than the following line from this article: Mrs May made do with a dowdier college and relaxed by watching “The Goodies”, a particularly dire comedy. Sacrilege! … Continue reading

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Elementary Class Groups Updated

In a previous post, I gave a short argument showing that, for odd primes p and N such that the p-class group of is non-trivial. This post is just to remark that the same argument works under weaker hypotheses, namely: … Continue reading

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Thoughts on Paris

Nothing is more pretentious or annoying than when an American offers, uninvited, their opinions of Paris. Here, then, are some of mine. Starting the day with a two hour lecture on elliptic integals: OUI: Who does not get a slight … Continue reading

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Who proved it first?

During Joel Specter’s thesis defense, he started out by remarking that the -expansion: is a weight one modular forms of level and moreover, for prime, is equal to the number of roots of modulo minus one. He attributed this result … Continue reading

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Return to Northwestern

Today I returned to Northwestern, taking part in both the communal faculty lunch and the post prandial espresso. Jared Wunsch worked his magic on the Silvia (Rancilio) to pour one of the best espressos I have had in a very … Continue reading

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