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Meta
Tag Archives: RLT
MSRI Now
Continuing on the theme of the last post (Buzzard related viral videos), you can now view Buzzard’s MSRI course (in progress at the time of this post) online here. Having previously excoriated MSRI for restricting how many people can attend … Continue reading
Posted in Mathematics
Tagged Brown, Drinfeld, Drinfeld Seminar, Kevin Buzzard, Local Langlands, Mariusz Wodzicki, Michael Harris, RLT, Weil Group
2 Comments
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
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
Posted in Mathematics
Tagged Contradictions, CSP, Fred Diamond, Fred Diamond's Beard, George Boxer, Ihara's Lemma, John Voight, Keerthi, Ken Ribet, Mathematica, Matthew Emerton, RLT, Serre
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Random Photos
Lunt Hall, the Northwestern mathematics building, recently underwent an upgrade of the fire alarm system. This includes introducing informative new signage, such as the following: Another change is that the “internal” window to my office was boarded up. The window … Continue reading
Posted in Waffle
Tagged Duke, Fire Alarm, Jonathan Wahl, Office Hours, Oracle at Delphi, RLT, Sarnak, TARDIS
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Harris 60
I’ve just returned from the excellent MSRI workshop which honored Michael Harris’ 60th birthday, and here is a brief summary of some of the gossip and mathematics I picked up when I was there. First, let me take note of … Continue reading
Posted in Mathematics, Uncategorized, Waffle
Tagged Akshay Venkatesh, Daniel Erman, David Geraghty, Kate Bekinsdale, Michael Harris, Patching, RLT, Taylor-Wiles
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The nearly ordinary deformation ring is (usually) torsion over weight space
Let \(F/{\mathbf{Q}}\) be an arbitrary number field. Let \(p\) be a prime which splits completely in \(F\), and consider an absolutely irreducible representation: \(\rho: G_{F} \rightarrow {\mathrm{GL}}_2({\overline{\mathbf{Q}}}_p)\) which is unramified outside finitely many primes. If one assumes that \(\rho\) is … Continue reading
Huuuuuge piles of cash
As widely reported today, the first of the “Breakthrough” prizes in mathematics have been announced. Leaving aside the question as to whether such awards are sensible (Persiflage is more sympathetic to capitalist principles than your average pinko marxist mathematician), I … Continue reading