Tag Archives: Matthew Emerton

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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Tensor Products

Let be an irreducible representation of a finite group Say that is tensor indecomposable if any isomorphism implies that either or is a character. In conversations with Matt and Toby (which permeate the rest of this post as well), the … Continue reading

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Harassed by Springer

Those of you who have ever submitted a paper to any mathematical journal may have noticed that it’s not a particularly speedy process. Nowadays, even a one year turnaround is nothing out of the ordinary. Thus, I always find it … Continue reading

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