Tag Archives: Matthew Emerton

Schaefer and Stubley on Class Groups

I talked previously about work of Wake and Wang-Erickson on deformations of Eisenstein residual representations. In that post, I also mentioned a paper of Emmanuel Lecouturier who has also proved some very interesting theorems. Today, I wanted to talk about … Continue reading

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Swimming Leaderboard

The first rule of number theory swim club is…talk about number theory swim club! Anyone can join, as long as you are a number theorist at the University of Chicago with a current gym membership. The standard meeting time is … Continue reading

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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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Pseudo-representations and the Eisenstein Ideal

Preston Wake is in town, and on Tuesday he gave a talk on his recent joint work with Carl Wang Erickson. Many years ago, Matt and I studied Mazur’s Eisenstein Ideal paper from the perspective of Galois deformation rings. Using … Continue reading

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Erdős Number 3!

My chances at this point of writing a paper with Erdős are probably very small. My chances of writing a paper with one of Erdős’ collaborators is also quite small. I had assumed that I had not even met — … Continue reading

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Artin No-Go Lemma

The problem of constructing Galois representations associated to Maass forms with eigenvalue 1/4 is, by now, a fairly notorious problem. The only known strategy, first explained by Carayol, is to first transfer the representation to a unitary group over an … Continue reading

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Serre 1: Calegari 0

I just spent a week or so trying to determine whether Serre’s conjecture about the congruence subgroup property was false for a very specific class of S-arithmetic groups. The punch line, perhaps not surprisingly, was that I had made an … Continue reading

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