Category Archives: Uncategorized

The stable cohomology of SL(F_p)

Back by popular demand: an actual mathematics post! Today’s problem is the following: compute the cohomology of for a (mod-p) algebraic representation. Step 0 is to say what this problem actually is. It makes sense to talk about certain algebraic … Continue reading

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Referee Requests

################################################### From: Mathematics Editorial Office Subject: [Mathematics] Review Request Date: December 26, 2018 at 7:43:31 AM CST Dear Professor Calegari, Happy new year. We have received the following manuscript to be considered for publication in Mathematics (http://www.mdpi.com/journal/mathematics/) and kindly invite … Continue reading

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Local-global compatibility for imaginary quadratic fields

One of the key steps in the 10-author paper is to prove results on local-global compatibility for Galois representations associated to torsion classes. The results proved in that paper, unfortunately, fall well-short of the optimal desired local-global compatibility statement, because … Continue reading

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Jacquet-Langlands and an old R=T conjecture

This is part 2 of a series of posts on R=T conjectures for inner forms of GL(2). (See here for part 1). (Edit: this is still incorrect and there should have been a part 3, but I’ve been distracted… in … Continue reading

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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

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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

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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

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