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Meta
Tag Archives: Richard Taylor
The horizontal Breuil-Mezard conjecture
Postdoc hiring season will be upon us soon! I have two excellent graduate students who will be applying for academic jobs soon, Chengyang Bao and Andreea Iorga. I have mentioned Chengyang’s first project before here and an introduction to the … Continue reading
Posted in Mathematics, Students, Work of my students
Tagged Andreea Iorga, Andrew Wiles, Ariane Mézard, Breuil-Mezard, Chengyang Bao, Christophe Breuil, Cohen-Macaulay, Galois Representations, Gorenstein, Hilbert, Hiring Season, Kevin Buzzard, Local Langlands, Mark Kisin, Richard Taylor, Sandra Rozensztajn, Taylor-Wiles, Toby Gee
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More on Lehmer’s Conjecture
Lehmer said it was a “natural question” whether there existed an integer such that \(\tau(n)=0\) or not. I’ve wondered a little bit recently about how reasonable this is. (See this post.) The historical context is presumably related to the fact … Continue reading
The Journal of Number Theory experiment
The Journal of Number Theory has been (for some time) the standard “specialist” journal for number theory papers. By that, I mean it was a home for reasonably good number theory papers which were not (necessarily) good enough for some … Continue reading
Posted in Mathematics, Politics
Tagged Algebra & Number Theory, Annals of Math, Botiques, Compositio, Duke, Elsevier, Inventiones, JNT, Jussieu, Richard Taylor
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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
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