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Meta
Tag Archives: David Helm
Local-global compatibility for imaginary quadratic fields
One of the key steps in the 10-author paper is to prove results on local-global compatibility for Galois representations associated to torsion classes. The results proved in that paper, unfortunately, fall well-short of the optimal desired local-global compatibility statement, because … Continue reading
Jacquet-Langlands and a new R=T conjecture
It is somewhat mysterious how one should formulate the Jacquet-Langlands correspondence integrally, particularly in the presence of torsion classes. Even the classical case has many subtleties including for example some results in this paper of Ribet. In the case of … Continue reading
Posted in Uncategorized
Tagged Akshay Venkatesh, Allen Cheng, David Helm, I have a subtle plan my lord, Jacquet-Langlands, Jeff Manning, Ken Ribet, R=T, torsion
4 Comments
And then there were 8:
News from Minnesota on the 8-author paper has arrived! http://math.uchicago.edu/~fcale/blog/8author.mp4
Posted in Mathematics
Tagged bloopers, David Helm, Matthew Emerton, Minnesota, Robert Langlands
3 Comments
New Results In Modularity, Christmas Update
It’s a Christmas miracle! Keen watchers of this blog will be happy to learn that the 10 author paper discussed here and here is now available. (And just in case you also missed it, you can also find the other … Continue reading
Update on Sato-Tate for abelian surfaces
Various people have asked me for an update on the status of the Sato-Tate conjecture for abelian surfaces in light of recent advances in modularity lifting theorems. My student Noah Taylor has exactly been undertaking this task, and this post … Continue reading
Posted in Mathematics, Students
Tagged Ana Caraiani, Andrew Sutherland, Andrew Wiles, Bao Le Hung, Christian Johansson, David Helm, Francesc Fité, Freydoon Shahidi, George Boxer, Henry Kim, Jack Thorne, James Newton, Kiran Kedlaya, Laurent Clozel, Michael Harris, Nick Katz, Noah Taylor, Patrick Allen, Peter Scholze, Potential Modularity, Richard Taylor, Sato-Tate, Serre, Toby Gee, Victor Rotger, Vincent Pilloni
3 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