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Meta
Category Archives: Uncategorized
Jacquet-Langlands and a new R=T conjecture
It is somewhat mysterious how one should formulate the Jacquet-Langlands correspondence integrally, particularly in the presence of torsion classes. Even the classical case has many subtleties including for example some results in this paper of Ribet. In the case of … Continue reading
Posted in Uncategorized
Tagged Akshay Venkatesh, Allen Cheng, David Helm, I have a subtle plan my lord, Jacquet-Langlands, Jeff Manning, Ken Ribet, R=T, torsion
4 Comments
A strange continuity
Returning to matters OPAQUE, here is the following problem which may well now be approachable by known methods. Let me phrase the conjecture in the case when the prime p = 2 and the level N = 1. As we … Continue reading
Posted in Uncategorized
Tagged Eigencurve, Galois Representations, Halo, Kevin Buzzard, Lloyd Kilford, OPAQUE, Robert Coleman
2 Comments
Irregular Lifts, Part II
This is the global counterpart to the last post. I was going to write this post in a more general setting, but the annoyances of general reductive groups got the better of me. Suppose we fix the following: A number … Continue reading
Posted in Uncategorized
Tagged Artin Conjecture, Galois Representations, Hodge-Tate, lifting, On the record
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Fan Mail
Edit: A previous version of this post has been edited upon request. Somewhat less salaciously, I received a Christmas card from an academic couple of whom I am absolutely sure I have never met. (I just checked my mailbox at … Continue reading
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 frisson … Continue reading
Posted in Uncategorized
Tagged Boot, Boris Bikes, Canard & Champagne, Clozel, Coffee Cuillier, Croissants, Divvy, Elliptic Integrals, Foie Gras, Fragments, Giverny, j-function, Jacques Tilouine, Klein, Kouign Amann, La Bourse et La Vie, Le Peleton Cafe, Monet, Orange, Passager, Paul Bert, Semilla, Strada, Telescope, Ten Belles, Third Wave Coffee, VĂ©libs, vitello tonnato
4 Comments
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
Posted in Uncategorized
Tagged espresso, Jared Wunsch, Joel Specter, Northwestern, Silvia Rancilio, Thesis
1 Comment
Report from MSRI and Berkeley
Having attended last Friday’s academic sponsors’ day at MSRI, I can provide a little more context concerning the issues expressed last time. But first, it’s time for the current edition of NAME AND SHAME: There are currently 105 universities which … Continue reading
Posted in Uncategorized
Tagged Andronicos, Babette, Blue Bottle Coffee, Brown, Cafe Rouge, Cesar's, Chez Panisse, Dipankar, Gregoire's, Jeffrey Brock, MSRI, NYU, Ogus, Pear Galette
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The class number 100 problem
Some time ago, Mark Watkins busted open the “class number n” problem for smallish n, finding all imaginary quadratic fields of class number at most 100 (the original paper is here) Although the paper describes the method in detail, it … Continue reading
Central Extensions and Weight One Forms
As mentioned in the comments to the last post, Kevin Buzzard and Alan Lauder have made an extensive computation of weight one modular forms in characteristic zero (see also here). Thinking about what that data might contain, I wondered about … Continue reading
Posted in Mathematics, Uncategorized
Tagged Alan Lauder, Cohen-Lenstra, Computations, Kevin Buzzard, modular forms, Schur Multiplier, Tate, weight one
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Ventotene, Part II
I promised to return to a more mathematical summary of the conference in Ventotene, and indeed I shall do so in the next two posts. One of the themes of the conference was bounding the order of the torsion subgroup … Continue reading
Posted in Uncategorized
Tagged Akshay Venkatesh, Borel, completed cohomology, Nicolas Bergeron, Peter Scholze, Serre, torsion
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