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Meta
Tag Archives: David Geraghty
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
Abandonware
For a young mathematician, there is a lot of pressure to publish (or perish). The role of for-profit academic publishing is to publish large amounts of crappy mathematics papers, make a lot of money, but at least in return grant … Continue reading
Posted in Mathematics
Tagged Abandonware, Akshay Venkatesh, Andrew Odlyzko, Bernard Woolley, David Geraghty, Dick Gross, Discriminant Bounds, Galois Representations, Imaginary Quadratic Fields, Jacquet-Langlands, John Voight, Lassina Dembélé, Matthew Greenberg, Peter Sarnak, Publishing, Taylor-Wiles, Under The Cosh, Yes Minister
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New Results In Modularity, Part I
I usually refrain from talking directly about my papers, and this reticence stems from wishing to avoid any appearance of tooting my own horn. On the other hand, nobody else seems to be talking about them either. Moreover, I have … Continue reading
Posted in Mathematics
Tagged Ana Caraiani, Andrew Wiles, Bao Le Hung, Blasius, David Geraghty, David Helm, Deligne, Don Blasius, Functoriality, Gowers, Jack Thorne, James Newton, Langlands, Laurent Clozel, Michael Harris, Modularity, Nuno Freitas, Patrick Allen, Peter Scholze, Port, Ramanujan, Reciprocity, RLT, Samir Siksek, Serre, The Triangle, Toby Gee
13 Comments
A non-liftable weight one form modulo p^2
I once idly asked RLT (around 2004ish) whether one could use Buzzard-Taylor arguments to prove that any representation: \(\rho: \mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q}) \rightarrow \mathrm{GL}_2(\mathbf{Z}/p^2 \mathbf{Z})\) which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). … Continue reading
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
Posted in Mathematics
Tagged Akshay Venkatesh, Artin Conjecture, Carayol, David Geraghty, Griffiths-Schmid Variety, l_0, Matthew Emerton, Notation
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Hilbert Modular Forms of Partial Weight One, Part III
My student Richard Moy is graduating! Richard’s work has already appeared on this blog before, where we discussed his joint work with Joel Specter showing that there existed non-CM Hilbert modular forms of partial weight one. Today I want to … Continue reading