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Meta
Tag Archives: James Newton
SL_n versus GL_n
I recently wrote a paper (with Toby Gee and George Boxer, see also here) on constructing regular algebraic automorphic representations \(\pi\) of (cohomological) weight zero and level one, and therefore also cuspidal cohomology classes in the cohomology of \(\mathrm{GL}_n(\mathbf{Z})\) for … Continue reading
Posted in Mathematics
Tagged AI, ChatGPT, Gaëtan Chenevier, George Boxer, Go, Grunwald-Wang Theorem, Hilbert modular forms, Jack Thorne, James Newton, Jean-Pierre Labesse, Joachim Schwermer, John Tate, Jürgen Rohlfs, Karen Vogtmann, la langue française, Laurent Clozel, Nasit Darshan, Pierre Colmez, Raghuram, Serre, Serre-Tate Correspondence, Stefan Patrikis, Tate, Toby Gee
1 Comment
The future is now; recap from Cetraro
I’ve just returned from the second Journal of Number Theory biennial conference in Italy. It’s always nice to get a chance to see slices of number theory one wouldn’t otherwise see at the conferences I usually go to (although this … Continue reading
New Results in modularity, Christmas Update II
Just like last year, once again saint Nick has brought us a bounty of treasures related to Galois representations and automorphic forms in the final week of the year. First there was this paper by Newton and Thorne, proving, among … Continue reading
Posted in Mathematics
Tagged Bloch-Kato, Christmas, Christos Anastassiades, Delta, Gan-Gross-Prasad, Jack Thorne, James Newton, Liang Xiao, Northwestern, Patrick Allen, Potassium, Rankin-Selberg, Selmer Groups, Steroids, Symmetric Powers, Tea, Wei Zhang, Xinwen Xhu, Yichao Tian, Yifeng Liu
6 Comments
Hausdorff Trimester Summer School, May 11-15, 2020
This post is to encourage both PhD students and any junior researchers who are interested to consider applying to a summer school on the arithmetic of the Langlands Program. (Some financial support will be available.) This is the first event … Continue reading
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
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