Tag Archives: Matthew Emerton

Artin No-Go Lemma

Posted on December 13, 2016 by Persiflage

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

Posted on October 18, 2016 by Persiflage

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

Posted on March 28, 2016 by Persiflage

Let \(W\) be an irreducible representation of a finite group \(G.\) Say that \(W\) is tensor indecomposable if any isomorphism \(W = U \otimes V\) implies that either \(U\) or \(V\) is a character. In conversations with Matt and Toby … Continue reading →

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Harassed by Springer

Posted on June 2, 2015 by Persiflage

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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How not to be wrong

Posted on May 7, 2015 by Persiflage

I recently finished listening to Jordan’s book “how not to be wrong,” and thought that I would record some of the notes I made. Unlike other reviews, Persiflage will cut through to the key aspects of the book which perhaps … Continue reading →

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Horizontal Vanishing Conjectures.

Posted on August 8, 2014 by Persiflage

Let \(F\) be a number field, and let \(\mathbf{G}\) be a reductive group over \(F\), and let \(\Gamma\) be a congruence subgroup of \(\mathbf{G}(\mathcal{O}_F)\). I can hear BC objecting that this doesn’t make sense without extra choices; if you have … Continue reading →

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En Passant IV

Posted on July 19, 2014 by Persiflage

My students Richard Moy and Joel Specter have uploaded their paper on partial weight one Hilbert modular forms, previously discussed here, to the ArXiv. Germany now leads the world in both soccer and perfectoid spaces. This is a recipe for … Continue reading →

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A Preview of Barbados/Bellairs

Posted on April 21, 2014 by Persiflage

This post is probably not so interesting unless you plan to travel to the Caribbean in a few weeks. The website for the conference is offline, so I thought I might update attendees on what might be happening, at least … Continue reading →

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Local representations occurring in cohomology

Posted on November 5, 2013 by Persiflage

Michael Harris was in town for a few days, and we chatted about the relationship between my conjectures on completed cohomology groups with Emerton and the recent work of Scholze. The brief summary is that Scholze’s results are not naively … Continue reading →

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Virtual Congruence Betti Numbers

Posted on September 27, 2013 by Persiflage

Suppose that \(G\) is a real semisimple group and that \(X = \Gamma \backslash G/K\) is a compact arithmetic locally symmetric space. Let us call a cohomology class tautological if it is invariant under the group \(G\). For example, if … Continue reading →

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